Free Mechanical Efficiency Calculator
This Mechanical Efficiency Calculator computes the ratio of useful output work (or power) to total input work (or power), expressed as a percentage. It applies to any machine — hydraulic jacks, gear trains, electric motors, engines, pulleys, and screws.
Enter input and output work (J) or power (W / kW) using the same unit for both. The calculator finds efficiency η = (W_out / W_in) × 100.
Formula: η (%) = (W_out / W_in) × 100. Use matching units (J, W, kW, hp) for both fields. Efficiency must be between 0% and 100% for a real machine. Values above 100% indicate a data-entry error.
Quick answer
Mechanical efficiency (η) is the percentage of input work or power that a machine converts into useful output, calculated as η = (W_out / W_in) × 100. A perfectly frictionless machine would have η = 100%, but all real machines lose some energy to friction, heat, vibration, or deformation, so efficiency is always less than 100%. For example, a hydraulic jack that receives 100 J of input work and delivers 80 J of output work has a mechanical efficiency of 80%. Efficiency is dimensionless and the same formula applies whether you use work (joules) or power (watts), as long as both are measured over the same time period.
Formula & method
η (%) = (W_out / W_in) × 100
- η — Mechanical efficiency, expressed as a percentage (0–100%)
- W_out — Useful output work (J) or output power (W) delivered by the machine
- W_in — Total input work (J) or input power (W) supplied to the machine
η = mechanical efficiency (%), W_out = useful output work or power, W_in = total input work or power. The ratio is the same whether you use joules (J) or watts (W) as long as both quantities use the same unit.
W_loss = W_in − W_out • W_out = η × W_in / 100
Energy lost to friction and heat. Rearranging the main formula lets you find the required input given a target output and known efficiency.
Examples
- Input
- W_in = 100 J, W_out = 80 J
- Result
- η = 80%
- Why
- η = (W_out / W_in) × 100 = (80 / 100) × 100 = 80%. The jack converts 80 J of the 100 J supplied into useful lifting work; the remaining 20 J is lost mainly to seal friction and fluid leakage.
- Input
- P_in = 500 W, P_out = 425 W
- Result
- η = 85%
- Why
- η = (P_out / P_in) × 100 = (425 / 500) × 100 = 85%. Power in watts can be used directly instead of joules because the time cancels. The motor dissipates 75 W as heat in the windings and bearings.
- Input
- W_in = 300 J, W_out = 210 J
- Result
- η = 70%
- Why
- η = (210 / 300) × 100 = 70%. Screw mechanisms typically achieve 25–75% efficiency due to high thread friction. Here 90 J (30%) is lost as heat along the thread surfaces.
- Input
- P_in = 75 kW, P_out = 60 kW
- Result
- η = 80%
- Why
- η = (60 / 75) × 100 = 80%. Both values are in kilowatts so no unit conversion is needed — the unit cancels. The 15 kW loss accounts for exhaust heat, friction, and accessory loads.
Frequently asked questions
What is mechanical efficiency?
Mechanical efficiency is the ratio of the useful work (or power) delivered by a machine to the total work (or power) put into it, expressed as a percentage. Because all real machines lose energy to friction, heat, and vibration, efficiency is always less than 100%. A value of 80% means the machine converts 80% of input energy into useful output.
What is the formula for mechanical efficiency?
The formula is η (%) = (W_out / W_in) × 100, where W_out is the useful output work or power and W_in is the total input work or power. The ratio is the same whether you supply joules, watts, kilowatts, or horsepower, as long as both values use the same unit.
Can mechanical efficiency ever be greater than 100%?
No. A mechanical efficiency above 100% would violate the first law of thermodynamics (conservation of energy), meaning the machine would create energy from nothing. Real machines always have efficiency below 100% because some input energy is inevitably lost to friction, heat, sound, or deformation.
What is the difference between mechanical efficiency and overall efficiency?
Mechanical efficiency considers only mechanical losses such as friction and windage inside a machine. Overall (or total) efficiency also includes electrical, thermal, and other conversion losses. For a motor-driven pump, mechanical efficiency covers just the pump head, while overall efficiency multiplies the motor's electrical efficiency by the pump's hydraulic and mechanical efficiencies.
How do I improve the mechanical efficiency of a machine?
The most effective steps are: lubricating moving parts to reduce friction, using roller or ball bearings instead of plain bushings, reducing the number of moving parts, tightening manufacturing tolerances to minimise leakage or slippage, and operating at the machine's designed load range. Even small reductions in friction can produce meaningful efficiency gains over time.
How is mechanical efficiency different from velocity ratio and mechanical advantage?
Velocity ratio (VR) is the ratio of input displacement to output displacement, and mechanical advantage (MA) is the ratio of output force to input force — both are purely geometric properties. Mechanical efficiency relates the two: η = MA / VR. If friction were zero, MA would equal VR and η would be 100%; real friction causes MA to fall below VR, reducing efficiency below 100%.
Sources & references
- Mechanical efficiency - Wikipedia
- Simple Machines - The Physics Classroom
- Machine efficiency and work - Khan Academy
External references open in a new tab. We are independent and not affiliated with these organizations.
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Provided “as is” for general information only — results may be inaccurate, so verify before you rely on them. No warranty; use at your own risk.
Built and reviewed by HIFreeTools against the formula shown above and any authoritative references cited on this page. See our methodology and editorial standards.
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