VFD Energy Savings Calculator (Variable Frequency Drive)

How the calculator works

The tool compares two ways of running the same motor. In the baseline, the machine runs at full motor speed and the flow is cut back some other way, with a throttling valve on a pump or a damper on a fan, which wastes energy by fighting the flow the motor is still making. In the second case, a variable frequency drive slows the motor itself so it only makes the flow you need, and the power falls with it. Enter the rated power, the load type, the average speed or a load profile, the hours, the motor and drive efficiencies, and the electricity price, and the panel reports the energy saved, the money saved, the CO2 avoided, the share of the energy cut, the simple payback, and the baseline and with-VFD energy for the year.

For a centrifugal pump or fan the heart of the calculation is the cube law. The VFD input power is rated power times the speed fraction cubed, divided by the motor efficiency and the drive efficiency: P = rated x (speed)^3 / (motor eff x VFD eff). The baseline power, with no drive and the flow throttled, is close to rated power divided by the motor efficiency, since a throttled centrifugal machine keeps drawing near its full power. Multiply each power by the operating hours and you have the annual energy each way, and the difference is the saving. On the default 30 kW fan at 80 percent speed, the baseline is 195,652 kWh a year and the drive cuts it to 103,272 kWh, a saving of 92,380 kWh, or about 47.2 percent of the drive energy.

For a constant-torque load the tool switches laws. A conveyor, a positive-displacement pump, or a screw or reciprocating compressor needs roughly the same torque at every speed, so its power varies with speed directly rather than with the cube. Slow one of these to 80 percent and the power falls to about 80 percent, not to half, so the VFD power becomes rated x speed / (motor eff x VFD eff). The saving is real but far smaller, and mixing the two load types up is the single most common mistake people make with a VFD savings estimate. The tool asks you to pick the load type so the number it reports matches the machine you run.

The load-profile mode is where the estimate gets honest. Very few machines sit at one speed all year, so instead of a single average you can enter rows of speed percent and hours per year, and the tool sums the energy over the rows. The VFD energy becomes the sum of hours times rated times speed cubed divided by the two efficiencies, and the baseline stays the total hours times rated divided by the motor efficiency. Summing over the real hours at each speed gives a truer saving than plugging in one average speed, because the cube law is not linear and the hours spent low count for far less energy than the hours spent high.

Money and emissions fall straight out of the energy. The money saved is the kWh saved times your electricity price, so 92,380 kWh at $0.12 is $11,086 a year. The CO2 avoided is the kWh saved times the grid emission factor in kilograms per kWh, so 92,380 kWh at 0.4 kg gives about 37.0 tonnes a year. If you enter the installed cost of the drive, the simple payback is that cost divided by the annual money saved, which on the default $6,000 drive is about 0.5 years. Those three outputs, the money, the carbon, and the payback, are what usually decide whether a drive gets bought, and the running cost also feeds the wider work in Energy Management.

The affinity laws for pumps and fans

The cube law is not a rule of thumb, it is one of the affinity laws, the set of relationships that govern how a centrifugal pump or fan behaves as you change its speed. There are three of them, and they always travel together. Flow varies in direct proportion to speed, so halve the speed and you halve the flow: Q is proportional to N. Head, the pressure the machine produces, varies with the square of the speed, so halve the speed and the head falls to a quarter: H is proportional to N squared. And the power the machine absorbs varies with the cube of the speed, so halve the speed and the power falls to an eighth: P is proportional to N cubed.

The power law is the one that makes a VFD worth buying. It is really the flow law and the head law multiplied together, because hydraulic power is flow times head, and speed times speed squared is speed cubed. That is why the saving is so large for a modest speed cut. At 80 percent speed the flow is 80 percent, the head is 64 percent, and the power is 0.8 cubed, which is 0.512, so the shaft draws only about 51 percent of its full power and you have saved roughly 49 percent by slowing down a fifth. The energy saving fraction of the pure curve is 1 minus speed cubed, and on the default that is 1 minus 0.512, close to the 47.2 percent the tool reports once the efficiencies are folded in.

The affinity laws hold well over the normal working range but they are an idealisation, and they lose accuracy at the extremes. Below about half speed the assumptions behind them start to drift, the motor and drive efficiencies fall off, and on a pump the flow can approach the point where it no longer overcomes the system it feeds. For most retrofit sizing the range from full speed down to about 50 percent is where the cube law earns its keep, and that is exactly the range where a VFD delivers the bulk of its savings anyway. The tool uses the cube law across the range you enter and flags high-static-head systems, where the affinity power law overstates the saving, as a case to treat with caution.

Why the power follows the cube

It helps to see why the exponent is three and not one, because that is what separates a fan from a conveyor. The useful work a pump or fan does each second is the flow it moves times the pressure it moves it against, flow times head. When you slow a centrifugal machine, both of those fall at the same time. The flow falls in step with speed because the impeller sweeps less volume per turn, and the head falls with the square of speed because pressure in a centrifugal machine goes with the tip speed squared. Multiply a quantity that scales with N by a quantity that scales with N squared and the product scales with N cubed.

A constant-torque machine is different because only one of those two factors moves. A conveyor belt, for example, needs roughly the same pulling force whether it runs fast or slow, since the weight on the belt does not change with speed. Force is like torque, and it stays put, so the power, which is torque times speed, varies only with the speed itself. That is a linear law, not a cube law, and it is why the same 80 percent speed that saves nearly half the energy on a fan saves only about a fifth on a conveyor. The physics of the load, not the drive, decides which law applies, and the drive simply delivers whatever the load demands.

This is also why throttling wastes so much. When you throttle a centrifugal pump with a valve instead of slowing it, the motor keeps spinning at full speed and the impeller keeps trying to make full head, so the power stays near the top of the curve while the valve burns off the excess as heat and noise. You have not reduced the work the motor does, you have added a restriction it has to push against. Slowing the motor with a VFD reduces the work itself, which is why the energy you recover is not a trickle but close to half on a machine that spends its life at part flow.

Simple average speed versus a load profile

The tool offers two ways to describe how the machine runs, and the choice matters more than it first looks. The simple mode takes one average speed, which is quick and fine for a machine that genuinely sits near one operating point, or for a first cut before you have measured anything. You enter the average speed and the hours and the tool applies the cube law once. It is the honest way to get a ballpark, and on many fans and pumps the ballpark is close enough to decide whether a fuller study is worth it.

The load-profile mode is the accurate way, because the cube law is not linear and an average hides the truth. Imagine a pump that spends half its hours at full speed and half at 50 percent. The naive average is 75 percent, which suggests a decent saving, but the real energy is dominated by the full-speed half where the cube law gives no saving at all, while the 50 percent half barely sips power. Summing the two blocks separately gives a very different, and correct, number. Whenever a machine swings across a wide range of speeds, enter the hours at each speed rather than one average, and let the tool add the blocks up.

Getting the profile is usually easier than people fear. A drive’s own display, a data logger, or the building management system will often give you the hours at each speed band over a representative period, which you then scale to a year. Even a rough three-line or four-line profile, so many hours near full speed, so many at part speed, so many idling low, beats a single average, because it captures the shape of the duty rather than smearing it. The third worked example below shows exactly this, a 45 kW pump split across three speed bands, and the number it produces is the one you can defend to a finance team.

Variable torque versus constant torque

Every VFD savings estimate turns on this one distinction, so it is worth being clear about which machines fall where. Variable-torque loads are the centrifugal family: centrifugal pumps, centrifugal and axial fans, blowers, and centrifugal compressors. Their torque rises with the square of speed and their power with the cube, so they are the loads where a VFD shines and where the cube law applies. If your machine moves a fluid by spinning an impeller or a bladed wheel, it is almost certainly variable torque, and the big savings are on the table.

Constant-torque loads are the machines that move a fixed load against a steady resistance: conveyors, hoists, positive-displacement pumps, screw and reciprocating compressors, mixers, extruders, and mills. Their torque is roughly the same at every speed, so their power rises only in proportion to speed. A VFD still helps a constant-torque machine, both for process control and for the energy saved when it genuinely runs slower, but the energy prize is a fraction of what a fan gives. Setting the load type to constant torque in the tool switches the law from the cube to the linear form and reports the smaller, truthful saving.

The fourth worked example makes the gap concrete. A 15 kW conveyor at 80 percent speed saves only about 17.5 percent of its energy, while the same 80 percent on a fan saves 47.2 percent. That is the difference between the cube law and the linear law at one speed, and it is why quoting fan savings on a conveyor, or the reverse, produces numbers that are wrong by more than a factor of two. Before you trust any VFD estimate, from this tool or any other, check that the load type is set to match the physics of the machine, because nothing else you enter matters as much.

Static head and where the cube law breaks down

The affinity power law assumes the pump or fan works against a purely frictional system, one where the resistance rises with flow and falls away to nothing as the flow stops. Many systems are not like that. A pump that lifts water to a fixed height, an elevated tank or a distant reservoir, works against static head, a fixed pressure that does not change with flow and does not disappear as you slow down. Static head puts a floor under the pressure the pump must make, and that floor is what breaks the clean cube law.

The effect is that a high-static-head pump cannot slow very far before it stops delivering flow at all. As you reduce speed, the head the pump can make falls with the square of speed, and once it drops to the static lift, the flow goes to zero even though the pump is still turning. Because the pump spends its reduced-speed life fighting a pressure that will not go away, the real energy saving is far below what the pure cube law promises. On a system that is mostly static head, a VFD may save little or nothing, and slowing the pump can even move it to a worse operating point.

This is why the tool carries a high-static-head flag and why the affinity result should be read as an upper bound on a lifting system. For a friction-dominated system, closed loops, air-handling ductwork, cooling-water circuits with little lift, the cube law is close to reality and the savings are as large as the tool shows. For a lifting system, use the load-profile mode, be conservative with the speed range, and treat the result as optimistic until a pump curve and a system curve confirm the real operating points. When in doubt, get the actual curves; static head is the classic reason a VFD retrofit under-delivers against a napkin estimate.

Motor and VFD efficiency

The cube law describes the shaft power, but the meter measures the electrical power, and two efficiencies sit between the two. The motor efficiency is the fraction of electrical power that reaches the shaft as mechanical work, typically 90 to 95 percent for an industrial induction motor and often stamped on the nameplate as an IE class. The VFD efficiency is the fraction the drive itself passes through after its own switching and conditioning losses, usually 96 to 98 percent at a decent load. The tool defaults to 92 percent motor and 97 percent drive, sensible middle values, and you should override them with your nameplate figures where you have them.

The drive does add a small loss that the throttled baseline does not carry, and the tool accounts for it honestly. In the baseline, the motor runs across the line with no drive, so only the motor efficiency applies. With the VFD fitted, the electrical power passes through both the drive and the motor, so both efficiencies apply, which is why the with-VFD power is divided by the product of the two. That drive loss is why a VFD gives back a little less than the pure shaft saving, and it is also why fitting a drive to a machine that runs flat out at full speed most of the time can actually cost energy rather than save it, because you pay the drive loss all year for a speed reduction you rarely use.

Efficiency also shifts with load, and that is worth remembering on a deep speed cut. Both the motor and the drive are most efficient near their rated load and lose a few points as the load falls, so a motor running at 30 percent of its rating is not as efficient as it is at 80 percent. For the normal working range the tool’s single efficiency figures are close enough, but if a machine spends long hours at very low speed, the true saving is a little below the ideal, because the efficiencies have sagged. This is one more reason the affinity laws are treated as accurate down to about half speed and as an optimistic guide below that.

CO2 avoided and simple payback

Once the energy saving is known, the carbon and the payback are simple arithmetic, but they are the numbers that carry the decision. The CO2 avoided is the energy saved times the grid emission factor, the kilograms of carbon dioxide released per kWh generated in your region. The tool defaults to 0.4 kg per kWh, a middling grid figure, and you should swap in your own grid’s factor, which ranges from near zero on a hydro or nuclear grid to well over 0.6 kg on a coal-heavy one. On the default, 92,380 kWh saved at 0.4 kg is about 37.0 tonnes of CO2 a year, the kind of figure that feeds a sustainability report or a scope-two emissions target.

The simple payback is the installed cost of the drive divided by the annual money saved, and on an energy-hungry machine it is often startlingly short. On the default $6,000 drive saving $11,086 a year, the payback is about 0.5 years, six months, after which the saving is pure return. That is why VFD retrofits on hard-running pumps and fans are among the most reliable energy projects a plant can take on. Simple payback ignores the time value of money, maintenance, and any control benefits, so it is a screening number rather than a full financial case, but when it comes back under a year it usually means the project is worth a closer look regardless.

Two cautions keep the payback honest. First, the saving depends heavily on the run hours and the load profile, so a machine that runs a few hundred hours a year, or one that sits at full speed most of the time, will show a much longer payback than the default even if it is a perfect centrifugal load. Second, the drive cost should be the installed cost, the hardware plus the wiring, the enclosure, any harmonic mitigation, and the commissioning, not just the price on the drive itself. Enter the real installed cost and the real profile, and the payback the tool gives is one you can take to a capital committee. The energy and cost savings also roll up naturally into the broader utility tracking in Energy Management.

What a VFD costs and where it fits

A variable frequency drive is a power-electronics box that sits between the supply and the motor and varies the frequency, and so the speed, of the motor. The hardware cost scales with the motor power, from a few hundred dollars for a small fractional-kilowatt drive to many thousands for a large one, and the installed cost usually runs well above the hardware alone once you add the enclosure, the cabling, any input reactor or harmonic filter, the control wiring, and the commissioning time. The tool’s default $6,000 for a 30 kW class drive is a reasonable installed figure, but get a real quote for your size, because the payback swings directly with it.

A drive earns its place wherever a centrifugal machine spends real time at part load. Building ventilation fans, cooling-tower fans, chilled-water and condenser-water pumps, boiler feed and process pumps, and induced and forced-draught fans are the classic wins, because they run long hours and rarely need full flow. Beyond the energy, a VFD brings soft starting that spares the motor and the driven machine from the shock of across-the-line starts, smooth process control that a throttling valve cannot match, and often a longer life for the whole train. Those benefits are real even where the energy saving is modest, which is part of why drives now appear on constant-torque machines too.

Where a drive earns little is the mirror image: a machine that runs flat out at full speed nearly all the time, a purely static-head lift, or a machine that runs so few hours a year that the saving never repays the cost. On those, the drive loss you pay all year can outweigh the speed reduction you rarely use. This tool exists to tell the two cases apart before you spend the money, by putting a defensible number on the saving for your machine, your profile, and your electricity price. It sits in the Industrial Automation silo alongside the machine-sizing tools, and its output feeds directly into the plant-wide energy picture in Energy Management.

Five worked examples

Example 1: fan at 80 percent speed (the default)

This is the case the tool opens on. A 30 kW centrifugal fan runs at 80 percent average speed for 6,000 hours a year, with 92 percent motor efficiency and 97 percent drive efficiency, at $0.12 per kWh. The baseline throttled fan uses 195,652 kWh a year, and the VFD cuts it to 103,272 kWh, a saving of 92,380 kWh, or $11,086 a year, avoiding 37.0 t of CO2. That is 47.2 percent of the drive energy gone, and a $6,000 drive pays back in about 0.5 years. The lesson: a modest 20 percent speed cut on a fan saves almost half the energy, because the power follows the cube of the speed and a small cut lands a large drop.

Example 2: pump slowed to 60 percent

A large 75 kW centrifugal pump runs at 60 percent average speed for 8,000 hours a year at $0.12 per kWh, with a $15,000 installed drive. Slowing a pump to 60 percent takes the power to 0.6 cubed, about 22 percent of full, so the saving is dramatic: 506,948 kWh a year, worth $60,834, and 202.8 t of CO2 avoided, which is 77.7 percent of the drive energy. The payback is about 0.2 years, roughly ten weeks. The lesson: a deep speed cut on a big, hard-running pump is the single biggest energy prize in most plants, and the more hours it runs and the deeper it slows, the faster the drive pays for itself.

Example 3: a real load profile

A 45 kW pump does not sit at one speed. It runs 1,500 hours a year at 100 percent, 4,000 hours at 75 percent, and 2,500 hours at 50 percent, 8,000 hours in total, at $0.12 per kWh with a $10,000 drive. Summing the cube-law energy over the three blocks gives a saving of 214,814 kWh a year, worth $25,778, avoiding 85.9 t of CO2, which is 54.9 percent of the drive energy, and a payback of about 0.4 years. The lesson: the honest number comes from the hours spent at each speed, not from one average. The full-speed hours save nothing while the half-speed hours save almost everything, and only summing the blocks captures that.

Example 4: constant-torque conveyor

A 15 kW conveyor is a constant-torque load, so it does not follow the cube. Running at 80 percent speed for 4,000 hours a year at $0.12 per kWh, with a $3,000 drive, it saves 11,430 kWh a year, worth $1,372, avoiding 4.6 t of CO2, which is only 17.5 percent of the drive energy, with a payback of about 2.2 years. The lesson: the same 80 percent speed that saved 47.2 percent on the fan saves only 17.5 percent here, because a conveyor holds roughly constant torque and its power falls only in proportion to speed, not with the cube. Set the load type honestly or the estimate is wrong by more than double.

Example 5: an imperial pump entered in HP

A 50 HP centrifugal pump, about 37.3 kW, runs at 70 percent speed for 5,000 hours a year at $0.12 per kWh, with an $8,000 drive. The tool takes the horsepower, converts it internally, and reports in kWh, money, and CO2 like any other case: 130,982 kWh saved a year, worth $15,718, avoiding 52.4 t of CO2, which is 64.6 percent of the drive energy, with a payback of about 0.5 years. The lesson: you can enter the motor in HP and still read the saving in kWh, money, and carbon, so a shop that thinks in horsepower does not have to convert anything by hand before it can size the opportunity.

Three expert tips

The cube law is a gift, but only for pumps and fans

The whole reason a VFD saves so much is the cube law, and it applies only to variable-torque centrifugal loads. A 20 percent speed cut on a centrifugal pump or fan saves about 49 percent of the shaft power, while the same cut on a constant-torque conveyor saves only about 20 percent. That is more than a factor of two, so the first thing to get right, before efficiency, hours, or price, is the load type. If you set a conveyor as a fan you will overstate the saving by more than double and buy a drive that never pays back. Identify whether the machine spins an impeller against a fluid or drags a fixed load against a steady resistance, and set the load type to match.

Static head steals the savings

A pump that lifts water to a fixed height carries static head, a pressure that does not fall away as you slow down, and that floor breaks the clean cube law. A high-static-head pump cannot slow far before the flow stops, so the real saving is far below the pure affinity number, sometimes only a fraction of it. Use the load-profile mode for these systems, be cautious with the speed range you assume, and read the affinity result as an upper bound until a pump curve and a system curve confirm the operating points. Friction-dominated systems, closed loops and ductwork with little lift, follow the cube law closely; lifting systems do not, and that is the classic reason a retrofit under-delivers.

Run hours and the load profile decide the payback

The saving is an energy per year, so it scales directly with how many hours the machine runs and how much of that time it spends slowed down. A drive on a fan that runs 8,000 hours a year at part load pays back in months, while a drive on a machine that sits at full speed most of the year barely pays at all, because you carry the drive loss all year for a speed reduction you rarely use. Measure the actual profile before you buy, using the drive display, a logger, or the building management system, and enter the real hours at each speed. A defensible payback comes from the true duty, not from an optimistic average speed and a full-time run assumption.

Limits of the method

This calculator gives a sound first estimate of the energy a VFD saves, not a finished engineering study. It applies the affinity cube law to variable-torque loads and a linear law to constant-torque loads, folds in the motor and drive efficiencies, and multiplies by the hours to get the annual energy, which is most of what a screening estimate needs. It assumes the affinity laws hold across the speed range you enter, a throttled or damper baseline that draws near full power, and single efficiency figures that do not sag with load. Those assumptions are close to reality for a friction-dominated centrifugal machine in its normal working range.

What it does not model is the detail a full study carries. It does not read a pump curve against a system curve, so it cannot find the exact operating points a high-static-head system lands on, and it treats static head only as a caution flag rather than a calculation. It does not track how the motor and drive efficiencies fall at very low load, so a deep, long-duration speed cut may save a little less than it shows. It does not price the harmonics, the cabling, or the control changes a real install needs beyond the single installed-cost figure you enter, and it uses simple payback rather than a discounted cash flow. Use the result to size and compare the opportunity, then confirm the operating points, the drive rating, and the installed cost against pump and system curves and a qualified engineer before you commit the capital.

Common mistakes to avoid

The first mistake is setting the wrong load type, quoting cube-law fan savings on a constant-torque conveyor or the reverse, which throws the number off by more than double. Always match the load type to the physics of the machine. The second is ignoring static head, applying the pure cube law to a pump that lifts water a fixed height and then wondering why the retrofit saves a fraction of what the estimate promised. Flag high-static-head systems and treat the affinity number as an upper bound until the curves confirm the operating points.

A third mistake is using one average speed for a machine that swings across a wide range, since the cube law is not linear and an average overstates the saving; enter a load profile instead. A fourth is assuming full-time operation, or guessing the run hours high, which inflates both the saving and the payback; measure the real hours before you buy. A fifth is fitting a drive to a machine that runs flat out at full speed nearly all the time, where the drive loss you pay all year outweighs the speed reduction you rarely use, so the drive costs energy rather than saving it. Match the load type, respect static head, use the real profile and the real hours, and reserve drives for machines that genuinely spend time at part load, and the saving this tool reports will hold up in practice.

Where this calculator fits

It suits anyone weighing a variable frequency drive without opening a full energy study. A facilities engineer looking at the ventilation fans or the chilled-water pumps can put a number on the saving before calling a vendor. A plant engineer building an energy-project list can screen a dozen machines quickly and rank them by payback. An energy manager preparing a business case can produce the kWh, the money, the carbon, and the payback in one place, in kW or HP and any currency. A student learning why pumps and fans are the classic VFD wins can watch the cube law move the number as the speed changes.

Because it separates the load types and offers a load profile, it also builds intuition. You can watch the saving collapse when you switch a fan to a conveyor at the same speed, or watch it climb as you deepen the speed cut on a pump, and see for yourself why the physics of the load, not the drive, sets the prize. For the machines the drive turns, the Conveyor Belt Speed and Motor Power Calculator sizes the motor power a belt actually needs, the Pneumatic Cylinder Force and Air Consumption Calculator covers the air-powered actuators next door, and the Air Receiver Tank Size and Compressed-Air Demand Calculator sizes the storage behind a shop compressor. A gear ratio and output speed tool and a servo and actuator sizing tool are on the way in this silo. The energy and cost this tool saves roll up into the plant-wide view in Energy Management.

Frequently asked questions

Sources, disclaimer, and editorial transparency

The affinity laws for centrifugal pumps and fans, the cube-law power relationship, the linear law for constant-torque loads, and the efficiency treatment described here follow recognized motor-system and pump-and-fan engineering practice, including the affinity laws as taught across pump and fan references and the motor-system efficiency guidance of the US Department of Energy and the Compressed Air and Gas Institute (CAGI). VFD input power is treated as rated power x (speed)^3 / (motor efficiency x VFD efficiency) for a variable-torque load and rated power x speed / (motor efficiency x VFD efficiency) for a constant-torque load, the throttled baseline as rated power / motor efficiency, the energy saving fraction of the pure fan curve as 1 – (speed)^3, and the simple payback as installed drive cost divided by annual money saved. The tool assumes the affinity laws hold across the entered speed range, a throttled or damper baseline near full power, and single efficiency figures. This calculator and guide are built and reviewed by the OpsCalculators team; see our Editorial Policy for how each tool is researched, built, and tested.

Results are accurate estimates for planning and education, not a substitute for a full energy study or an engineering review. The method applies the affinity cube law to variable-torque loads and a linear law to constant-torque loads, but it does not read a pump curve against a system curve, treats static head only as a caution flag rather than a calculation, does not model how the motor and drive efficiencies fall at very low load, and uses simple payback rather than a discounted cash flow. High-static-head systems in particular save far less than the pure cube law suggests, so treat the affinity result as an upper bound there. Confirm the operating points, the drive rating, and the installed cost against pump and system curves, the manufacturer’s data, and a qualified engineer before you commit the capital. See our full Disclaimer. OpsCalculators.com is operated by MAFHH INTERNATIONAL LTD. Your inputs are processed in your browser and are never stored; see our Privacy Policy.