Machine Efficiency Calculator
Compute mechanical, electrical or thermal efficiency using η = Output / Input — with three-way solving for efficiency, output or input, a live energy-flow schematic, and companion loss, cost and lifecycle metrics.
Efficiency is the ratio of what you get to what you paid
Every real machine dissipates some of the energy that enters it — as heat from electrical resistance, friction in bearings, windage from rotating parts, iron losses in magnetic circuits, or incomplete combustion in engines. The efficiency is the fraction that survives as useful output. A motor that draws 50 kW and delivers 45 kW of shaft power is 90 % efficient; the missing 5 kW has been converted into heat, and it must be removed by the cooling system or it will eventually damage the machine. High efficiency therefore means both lower operating cost and less waste heat to manage.
Efficiency is not constant — it depends on load
The η = Pout/Pin formula treats efficiency as a single number, but in reality efficiency varies with load, speed and operating conditions. A motor running at 25 % of rated load may be only 60 % efficient, while the same motor at 75 % load is 92 % efficient. Transformers peak near full load; internal combustion engines peak in a narrow band of speed and torque. This is why machines are selected to operate near their design point — running a large motor at very light load wastes energy even though its nameplate efficiency looks high. Variable-speed drives and proper sizing are the two main tools for keeping real-world efficiency close to the peak value.
Small efficiency gains compound over a lifetime
A 1 % improvement in efficiency on a 100 kW motor running 8,000 hours per year saves 8,000 kWh of electricity per year — about €1,200 at €0.15/kWh. Over a 20-year life, that is €24,000, often more than the entire cost of the motor itself. This is why the purchase price of an electric motor is typically only 1–3 % of its total lifetime cost; the rest is the energy it consumes. The same arithmetic applies to pumps, fans, compressors and transformers, and it is the reason efficiency standards (IE3, IE4, IE5 for motors) have become a regulatory requirement in most developed economies.
η > 1 is possible for heat pumps, not for engines
For a machine that converts energy — motor, engine, turbine, transformer — efficiency is strictly less than 1 because some input energy is always degraded to low-grade heat. But for a heat pump or air conditioner, the useful output is heat moved, not energy converted, and it can far exceed the electrical input. The correct metric is the coefficient of performance (COP), not efficiency: a COP of 3 means 3 kW of heat delivered for every 1 kW of electricity consumed. The energy balance is preserved — the extra 2 kW comes from the cold reservoir — but the ratio Pout/Pin is greater than 1. This distinction is important when comparing technologies; a heat pump at COP 3 uses about a third as much primary energy as a resistive heater producing the same heat.
How to Use This Calculator
The efficiency relation links three quantities: η, Pout and Pin. Pick which one you want the tool to solve, then fill in the other two.
1. Choose what to solve for
Pick η, Pout or Pin from the toggle. The calculator rearranges η = Pout/Pin automatically for whichever variable you choose.
2. Choose your reporting format
Efficiency can be reported as a percentage (0–100 %) or as a fraction (0–1). The toggle switches between them; internally the calculation always uses the fraction and converts on the way in and out.
3. Use realistic presets
Presets cover typical values: efficiency from 5 % (incandescent bulb) to 99.5 % (large transformer), output from 0.1 kW (small appliance) to 1,000 kW (industrial motor), and input from 0.2 kW to 2,000 kW.
4. Read the result and verdict
The result card shows the solved value plus the losses, the fraction form and the loss fraction. A colour-coded verdict classifies the efficiency from very low through low, moderate, high, very high, excellent and near-ideal.
5. Check the schematic and charts
The schematic shows the energy flow: input arrow into the machine, output arrow out the top, loss arrow out the bottom, plus a proportional bar showing the split between useful output and losses. The main chart plots η against output for three input levels.
6. Switch to Advanced for depth
Advanced mode adds a η vs. input chart, a sensitivity analysis, and companion metrics — losses in kW and BTU/h, annual energy use, annual cost and annual cost of losses, CO₂ emissions, and equivalent operating hours — all with editable hours/year and electricity rate.
What This Tool Offers
Built around the classic efficiency relation η = Pout / Pin, the fundamental link between useful output, total input and losses in any energy-converting machine.
Three-way solving
Solve for efficiency, output power, or input power. The calculator rearranges the formula for whichever variable you choose.
Percentage or fraction
Report efficiency as a percentage (0–100 %) or as a fraction (0–1). The toggle switches between them while the calculation stays consistent.
Live energy-flow schematic
A Sankey-style diagram with input flowing into the machine, output and losses emerging from it, and a proportional bar showing exactly how the input energy splits between the two.
Efficiency-class verdict
Each result is classified from very low through low, moderate, high, very high, excellent and near-ideal, with a coloured badge referencing typical machines.
Companion loss & cost metrics
Losses in kW, hp and BTU/h; annual energy and cost; annual cost of losses; CO₂ emissions; and equivalent running hours — all editable for hours/year and rate.
Reference tables
An efficiency lookup grid, typical efficiencies by machine type, and a full variable reference with the temperature, load and unit notes.
Reference Tables & Conversions
A quick three-field solver, an efficiency lookup grid, and typical values by machine type.
Quick efficiency solver — enter any two, read the third
Efficiency Lookup — Pout vs. Pin
Computed from η = Pout / Pin × 100. Values in percent.
| Pout (kW) | Pin = 10 | Pin = 50 | Pin = 100 | Pin = 500 | Pin = 1000 | Pin = 5000 |
|---|
Typical Efficiencies by Machine Type
Representative peak efficiencies at rated load. Actual efficiency varies with load, speed, size and operating conditions.
| Machine type | Typical η (%) | Typical η (fraction) | Notes |
|---|---|---|---|
| Large power transformer (100 MVA) | 99.5 – 99.7 | 0.995 – 0.997 | Highest efficiency of any common machine |
| Distribution transformer (100 kVA) | 98.5 – 99.2 | 0.985 – 0.992 | Slightly lower at small size |
| Large synchronous generator | 98 – 99 | 0.98 – 0.99 | Utility-scale generation |
| Industrial induction motor (IE4, 75 kW) | 95 – 97 | 0.95 – 0.97 | Premium efficiency class |
| Standard induction motor (IE2, 75 kW) | 92 – 94 | 0.92 – 0.94 | Older standard, being phased out |
| Small induction motor (1 kW, IE3) | 82 – 88 | 0.82 – 0.88 | Efficiency drops sharply at small size |
| Permanent-magnet brushless motor | 92 – 96 | 0.92 – 0.96 | Dominates EV and drone propulsion |
| Large steam turbine (utility) | 40 – 50 | 0.40 – 0.50 | Limited by Carnot cycle and steam conditions |
| Combined-cycle gas turbine plant | 55 – 62 | 0.55 – 0.62 | Highest of any fossil-fuel generator |
| Simple-cycle gas turbine | 30 – 42 | 0.30 – 0.42 | Lower than combined-cycle; used for peaking |
| Large diesel engine (marine, 50 MW) | 48 – 52 | 0.48 – 0.52 | Best of any combustion engine |
| Automotive petrol engine (at best BSFC point) | 35 – 42 | 0.35 – 0.42 | Peak only; typical driving 15–25 % |
| Automotive diesel engine (at best BSFC point) | 40 – 45 | 0.40 – 0.45 | Higher than petrol due to compression ratio |
| Small petrol engine (lawnmower, generator) | 20 – 28 | 0.20 – 0.28 | Efficiency drops sharply at small size |
| Pumped-hydro storage (round-trip) | 70 – 80 | 0.70 – 0.80 | Includes both pump and turbine losses |
| Lithium-ion battery (round-trip) | 85 – 95 | 0.85 – 0.95 | Depends on C-rate and temperature |
| Electrolyser (PEM, hydrogen) | 65 – 80 | 0.65 – 0.80 | Falling cost and rising efficiency |
| Fuel cell (PEM, hydrogen) | 50 – 60 | 0.50 – 0.60 | Higher in CHP configuration |
| Centrifugal pump (large, best efficiency point) | 80 – 88 | 0.80 – 0.88 | Drops sharply away from BEP |
| Large industrial fan (backward-curved) | 75 – 85 | 0.75 – 0.85 | Lower for small or forward-curved types |
| Reciprocating air compressor | 60 – 75 | 0.60 – 0.75 | Screw compressors 65–80 % |
| Incandescent light bulb | 3 – 5 | 0.03 – 0.05 | Most input becomes heat, not light |
| Halogen bulb | 5 – 8 | 0.05 – 0.08 | Marginal improvement over incandescent |
| Compact fluorescent (CFL) | 15 – 22 | 0.15 – 0.22 | Includes ballast losses |
| LED lamp (white, complete fixture) | 25 – 40 | 0.25 – 0.40 | Continues to improve; best LEDs near 50 % |
| Solar PV panel (commercial, at STC) | 18 – 24 | 0.18 – 0.24 | Shockley-Queisser limit ~33 % for single junction |
| Wind turbine (modern, at rated wind) | 40 – 50 | 0.40 – 0.50 | Betz limit 59.3 % for any wind turbine |
| Heat pump / air conditioner (COP) | 200 – 500 | 2.0 – 5.0 | Not true efficiency — heat moved, not converted |
| Human muscle (mechanical work / food energy) | 20 – 25 | 0.20 – 0.25 | Rest of food energy becomes heat |
Variable Reference
| Symbol | Meaning | Typical range | Units |
|---|---|---|---|
| η | Efficiency | 0 – 1 (or up to 5 for heat pumps) | — |
| η% | Efficiency as percentage | 0 – 100 (or up to 500) | % |
| Pout | Useful output power | 0.0001 – 10⁹ | kW (or any consistent unit) |
| Pin | Total input power | 0.0001 – 10⁹ | kW (or any consistent unit) |
| Ploss | Loss power = Pin − Pout | — | kW |
| L | Loss fraction = 1 − η | 0 – 1 | — |
| COP | Coefficient of performance (heat pumps) | 2 – 5 | — |
| kWh | Energy = power × time | — | kWh |
What Does η = Output / Input Measure?
Efficiency is the ratio of what a machine delivers to what it consumes. It is a dimensionless number between 0 and 1 for any machine that converts energy from one form to another — mechanical to mechanical, electrical to mechanical, chemical to thermal, or any other conversion. The complement of efficiency, the loss fraction, is the proportion of the input that has been degraded into low-grade heat and is no longer available to do useful work. In a motor, that loss appears as heat in the windings and bearings; in a transformer, as heat in the core and coils; in an engine, as heat rejected through the exhaust and radiator. Understanding where the losses go, and how they scale with load, is the starting point for any serious energy efficiency project.
The formula is deceptively simple. Because efficiency is defined as a ratio, it is independent of the size of the machine and independent of the units used for output and input — a 1 kW motor and a 1 MW motor can both be 95 % efficient, and the same efficiency holds whether you measure power in watts, kilowatts, horsepower or BTU/h, provided you use the same unit for both output and input. This is what makes efficiency such a useful universal metric: it lets you compare machines of very different sizes, technologies and applications on a common scale.
Efficiency Formula
The defining relationship is:
As a percentage, the same relation reads:
Rearranged to solve for the other two unknowns:
Pin = Pout / η
Useful derived quantities:
Loss fraction: L = 1 − η
Annual energy: E = Pin · hours / 1000 (MWh)
Annual cost of losses: C = Ploss · hours · rate (currency)
For heat pumps and cooling machines, the useful metric is coefficient of performance:
Efficiency Variables
| Symbol | Meaning | Notes |
|---|---|---|
| η | Efficiency (fraction) | Dimensionless, 0 to 1 for energy-converting machines |
| η% | Efficiency (percentage) | Same value multiplied by 100 |
| Pout | Useful output power | The work or power actually delivered to the load |
| Pin | Total input power | All energy or power drawn by the machine |
| Ploss | Loss power | Pin − Pout; appears as heat, sound or vibration |
| L | Loss fraction | 1 − η; the complement of efficiency |
| COP | Coefficient of performance | For heat pumps; may exceed 1 because heat is moved |
How Each Variable Affects the Result
The relation is linear in output and inverse-linear in input. Increasing output while holding input constant raises efficiency proportionally — a motor that delivers more shaft power from the same electrical input is simply more efficient. Increasing input while holding output constant lowers efficiency inversely — a machine that draws more power to do the same job is less efficient, and the extra power appears as additional losses. This is the arithmetic behind every efficiency improvement project: either increase the useful output at fixed input (better design, better materials), or reduce the input required for a given output (lower losses).
Efficiency is strictly less than 1 for any real energy-converting machine because some fraction of the input is always degraded. The second law of thermodynamics sets upper bounds on how close to 1 you can get — the Carnot efficiency for heat engines, the Betz limit for wind turbines, the Shockley-Queisser limit for single-junction solar cells. But within those limits there is enormous room for improvement, and the practical efficiency of a machine depends on its size, its load, its temperature, the quality of its materials, and the precision of its manufacturing. A large transformer at 99.7 % is not fundamentally different in physics from a small one at 95 % — the difference is almost entirely in the ratio of surface area to volume, which determines how much material can be devoted to reducing losses.
In practice, efficiency is rarely measured as a single value. It is a function of load, speed, temperature and supply voltage, and it peaks at the design point. Motors peak near 75 % load; transformers peak near full load; turbines peak at their design speed ratio. This is why oversizing a machine "for safety" is usually counterproductive: a 100 kW motor running at 20 kW load will be much less efficient than a properly sized 25 kW motor at the same load, and it will also have a worse power factor. The correct sizing rule is to select the machine for the load it will actually see, not for the maximum it might theoretically encounter.
Efficiency Calculation Examples
η = 45 / 50 = 0.9000 = 90.00 %
Losses = 50 − 45 = 5 kW = 10 % of input
Pout = 0.92 × 15 = 13.80 kW
Losses = 15 − 13.8 = 1.20 kW
Pin = 7.5 / 0.88 = 8.523 kW
Losses = 8.523 − 7.5 = 1.023 kW
Losses = 50 × 0.10 = 5 kW
Annual loss energy = 5 × 4,000 = 20,000 kWh
Annual cost of losses = 20,000 × 0.15 = €3,000/year
Quseful = 3.5 × 2 = 7 kW of heat
(The extra 5 kW is drawn from the outdoor air, not created.)
Frequently Asked Questions
Because real machines always have losses. Mechanical friction in bearings and seals converts kinetic energy into heat. Electrical resistance in copper windings converts electrical energy into heat. Magnetic hysteresis and eddy currents in iron cores convert magnetic energy into heat. Windage and turbulence in fluids convert kinetic energy into heat. Combustion inefficiency in engines leaves unburned fuel and rejects heat through the exhaust. In every case, some fraction of the input energy is degraded into low-grade heat that cannot be recovered to do useful work. The second law of thermodynamics guarantees that this degradation is unavoidable in any real process, so 100 % efficiency is thermodynamically impossible. The practical question is how close to 100 % a given machine can get, which depends on its size, materials, design and operating point.
For a machine that converts one form of energy into another, no — that would violate the first law of thermodynamics. But for a heat pump or air conditioner, the useful output is heat moved from a cold reservoir to a hot one, not energy converted. A heat pump with a COP of 3 delivers 3 kW of heat for every 1 kW of electricity consumed; the extra 2 kW comes from the outdoor air (or ground, or water), not from nowhere. The energy balance is preserved at the system level. The reason we do not call this "efficiency > 100 %" is that efficiency is defined for conversion, not for transport. The correct metric for a heat pump is the coefficient of performance, or COP, which is expected to be well above 1. Regulators sometimes express this as a "seasonal performance factor" (SPF) or "primary energy ratio" to avoid confusion with efficiency.
Efficiency is not a constant. For an electric motor, η rises from near zero at no load to a peak at around 75 % of rated load, then falls slightly as load increases further toward 100 %. The reason is that losses are split into two kinds: fixed losses (iron losses, friction, windage) that do not depend on load, and variable losses (copper losses, which go as load squared) that do. At light load, fixed losses dominate and efficiency is low. At rated load, the two are roughly balanced and efficiency is at its peak. Beyond rated load, the copper losses dominate and efficiency falls again. The same shape applies to transformers, pumps, fans and most rotating machines. This is why running a large motor at light load wastes energy, and why proper sizing matters as much as nominal efficiency class.
Efficiency (η) measures how much of the input power is converted into useful output power, regardless of whether the input is real (kW) or apparent (kVA). Power factor (PF) measures how much of the apparent power (kVA) drawn from the supply is real power (kW) that actually does work: PF = kW / kVA. A motor running at 90 % efficiency and 0.85 PF draws 100 kW of electrical input if it delivers 90 kW of shaft power, but the apparent power it presents to the supply is 100/0.85 = 117.6 kVA. The extra apparent power does not consume energy — it just circulates between the supply and the motor's magnetic field — but it does load the supply conductors and transformers. Both metrics matter for industrial plants: efficiency determines the energy bill, power factor determines whether the utility applies a penalty or requires a capacitor bank.
Because efficiency depends on the ratio of volume to surface area, and that ratio gets worse as machines get smaller. A large machine has a lot of volume — where the useful work happens — and comparatively little surface area — where losses escape. A small machine has proportionally more surface and less volume, so losses are a larger fraction of the total. This is why a 10 MW generator can reach 98.5 % efficiency while a 1 kW motor struggles to reach 88 %. The same principle applies across technologies: a large transformer is more efficient than a small one, a utility-scale gas turbine more efficient than a small one, a big cargo ship's diesel engine more efficient than a lawnmower's petrol engine. The practical consequence is that centralising generation and industrial processes generally improves efficiency, while distributed small-scale generation and appliances are typically less efficient per unit of output.
Start by understanding where the losses are. For a motor, the losses split roughly into copper (resistive) losses, iron (magnetic) losses, friction and windage, and stray load losses. Copper losses fall when the motor runs at lower current; iron losses are roughly constant; friction and windage rise with speed. The three highest-leverage actions are usually: (1) run the machine closer to its design point — a pump running at 25 % flow should be trimmed or speed-controlled rather than throttled; (2) reduce oversizing — replace a 100 kW motor running at 20 kW with a properly sized 25 kW unit; (3) upgrade to a higher efficiency class — IE4 motors are typically 2–4 percentage points more efficient than IE2 at the same size. Beyond these, maintenance matters enormously: a pump with a worn impeller or a motor with clogged cooling passages loses efficiency rapidly, so regular inspection and cleaning often delivers more savings than a capital replacement.
The lifetime cost of a machine is dominated by the energy it consumes, not by its purchase price. For an industrial motor running continuously, the purchase price is typically 1–3 % of the twenty-year total cost of ownership, while energy is 95 % or more. A 1 % improvement in efficiency on a 100 kW motor running 8,000 hours per year at €0.15/kWh saves 8,000 × 0.15 × 0.01 × 100 = €1,200 per year, or €24,000 over a 20-year life — more than the cost of the motor itself. This is why energy efficiency regulations focus on lifetime cost rather than purchase price, and why premium-efficiency equipment often pays for itself in a few years even with a significant price premium. The same logic applies to compressors, pumps, fans, boilers and transformers, and it is the economic basis of every industrial energy audit.
It depends on the machine type and size. For an industrial motor above 50 kW, target at least 95 % (IE3) and preferably 96 % (IE4). For a small motor below 1 kW, 85 % is realistic and 90 % is excellent. For a transformer, 98 % is the minimum and 99 % is achievable above 100 kVA. For a pump, target within 5 percentage points of the best-efficiency point (BEP) at the intended operating flow. For a combustion engine, the peak efficiency is what matters but the actual operating efficiency depends on the duty cycle. In every case, be realistic about the losses you cannot eliminate — the manufacturer's data sheet is a starting point, but the actual installed efficiency depends on the load profile, the power quality, the temperature and the maintenance. Design for the operating point, not for the nameplate.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| eta | Efficiency | % |
| Output | Useful output energy or power | |
| Input | Total input energy or power (same units as output) |
What it means
Machine efficiency is a measure of how effectively a machine converts input energy into useful output energy. It is defined as the ratio of output power (or work) to input power (or work), multiplied by 100 to express as a percentage: η = (P_output / P_input) × 100%. Losses occur due to friction, heat dissipation, vibration, noise, and other irreversibilities. Efficiency is always less than 100% in real machines. It is crucial for energy management: higher efficiency means lower operating costs and reduced environmental impact. In design, engineers strive to improve efficiency through better materials, lubrication, and design optimisation. Efficiency is used to compare different machines and to select the most suitable one for a given application. It is also a key parameter in system analysis, where overall efficiency is the product of component efficiencies. In power generation, efficiency determines fuel consumption and emissions. Regular maintenance is needed to sustain efficiency over time.
Worked example
Machine Efficiency – Two Examples
Real‑World| Parameter | Value |
|---|---|
| Input | 100 kW |
| Output | 90 kW |
| Parameter | Value |
|---|---|
| Input | 10 kW |
| Output | 8.5 kW |
Common mistakes
- Output and Input: Must be in the same units (Watts, kW, etc.).
- Efficiency < 100%: Always less than 1 (or 100%) due to losses.
- Mechanical vs. thermal efficiency: This is overall efficiency; for engines, distinguish thermal and mechanical.
- Losses: Do not forget to account for friction, heat, etc.
- Multiply by 100: If you want a percentage, multiply by 100; otherwise keep as a fraction.
Applications
Machine efficiency is the ratio of output power to input power, expressed as a percentage. It is a critical performance metric for all mechanical and electrical systems, from motors and pumps to engines and transmissions. High efficiency reduces energy consumption, operating costs, and environmental impact. Engineers use efficiency calculations to evaluate design alternatives, identify losses, and implement improvements. In industry, efficiency is monitored for predictive maintenance and energy management. The concept is also central to life‑cycle analysis and sustainability assessments. By improving efficiency, engineers can contribute to global energy conservation efforts and comply with regulatory standards.
- Electric motor and generator performance evaluation
- Pump and compressor efficiency analysis
- Internal combustion engine efficiency improvement
- HVAC system energy auditing
- Design of energy‑efficient industrial processes
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