Mechanical Efficiency Calculator
Find the efficiency of a machine from useful output and total input — either as work/energy or as power. A live 3D scene and charts show where the lost energy goes.
Reviewed by the ToolNestr Editorial Team — July 2026
Two ideas that trip students up
1. Input energy splits into two paths
All input energy (left box) goes somewhere: most becomes useful output (larger box), the rest is wasted as heat (smaller box) — at 80% efficiency, an 80/20 split.
2. Efficiency across machine types
Bar heights compare typical efficiency for an electric motor (~90%), a pulley system (~80%) and a combustion engine (~35%) — more moving parts and heat losses mean lower efficiency.
Efficiency graphs
How it works
The core idea in one line: mechanical efficiency is the fraction of input work or power a machine actually delivers as useful output — the rest is lost, almost always to friction as heat.
η = (Wout / Win) × 100%
from useful vs total work
η = (Pout / Pin) × 100%
from useful vs total power
η = (AMA / IMA) × 100%
actual vs ideal mechanical advantage
Rearranged, the work form solves any variable: W_out = η × W_in and W_in = W_out / η. The power form works the same way with P_out and P_in. Because output can never exceed input for a passive machine, η is always between 0% and 100%.
Worked example 1 — pulley system
Given: You do 500 J of work pulling a rope to lift a load, and the load gains 400 J of gravitational potential energy. Find the efficiency.
Worked example 2 — electric motor
Given: A motor draws 250 W of electrical power and delivers 210 W of mechanical power at its shaft. Find the efficiency and the power lost as heat.
The 40 W difference does not vanish — it converts to heat in the windings and bearings.
Typical efficiency of common machines
Real machines lose energy to friction, air resistance, and heat — the more moving parts, the more loss.
| Machine | Typical η | Main energy loss |
|---|---|---|
| Electric motor | 85–95% | Winding resistance, bearing friction |
| Bicycle drivetrain | 95–98% | Chain friction |
| Pulley system (with friction) | 70–90% | Rope/pulley friction |
| Internal combustion engine | 20–35% | Heat, exhaust, friction |
| Incandescent light bulb | ~5% | Heat (only ~5% becomes light) |
η = (useful output ÷ total input) × 100%. No real machine reaches 100% because some input always converts to heat.
Where mechanical efficiency actually matters
🔧 Engine and motor design
Engineers compare engine and motor efficiency to choose the most cost-effective option per watt delivered, and to meet fuel-economy or energy-rating standards.
🚲 Simple machines
Pulleys, levers, and inclined planes are rated by efficiency to show how much of your effort actually goes into moving the load, versus fighting friction in the mechanism itself.
💡 Energy ratings
Appliance efficiency ratings (motors, lighting, HVAC) are built on this same input/output ratio, guiding consumers and regulators toward lower energy waste.
Common misconceptions
"A well-built machine can reach 100% efficiency."
Never in practice — the second law of thermodynamics guarantees some energy converts to heat via friction or resistance in every real mechanism. Only an idealised, frictionless machine reaches 100%, and only on paper.
"Efficiency and mechanical advantage are the same thing."
Mechanical advantage compares output force to input force; efficiency compares output energy/work to input energy/work. A machine can have a large mechanical advantage and still be inefficient if friction wastes a lot of the input work.
"Lost energy just disappears."
Energy is conserved — the input that does not become useful output converts to another form, almost always heat (and sometimes sound or deformation), not nothing.
"Efficiency can be negative or over 100%."
For a passive machine, output can never exceed input, so η is always between 0% and 100%. A figure above 100% signals a measurement error or an external energy source not accounted for.
Formula sources & further reading
The formulas here are standard, traceable to:
- • OpenStax, University Physics Volume 1 — work, energy, and the conservation of energy. openstax.org
- • Halliday, Resnick & Walker, Fundamentals of Physics — work, energy, and power.
- • Serway & Jewett, Physics for Scientists and Engineers — energy methods and efficiency of machines.
η = (useful output ÷ total input) × 100%, using matching units (work-to-work or power-to-power). Results are rounded for display.
How to use this calculator
Pick the mode
"From work" for one-off energy transfers; "From power" for continuous machines like motors.
Enter two values
Fill any two of the three fields; the third solves live.
See the energy split
Use the sliders to watch the 3D scene show useful output vs wasted input.
Related tools
Frequently asked questions
What is mechanical efficiency?
Mechanical efficiency (η) is the ratio of useful output (work, energy, or power) a machine delivers to the total input it receives, expressed as a percentage: η = (output ÷ input) × 100%. No real machine reaches 100% because some input is always lost, usually to friction and heat.
How is efficiency calculated from work?
η = (W_out ÷ W_in) × 100%, where W_out is the useful work delivered (e.g. lifting a load) and W_in is the total work put in (e.g. the effort force times the distance you pushed). The difference, W_in − W_out, is wasted as heat, sound, or deformation.
How is efficiency calculated from power?
η = (P_out ÷ P_in) × 100%, the power version of the same ratio. This is common for motors and engines, where input and output are measured as rates (watts) rather than one-off amounts of work.
Why is mechanical efficiency always less than 100%?
The second law of thermodynamics guarantees some energy converts to non-useful forms — usually heat from friction — in every real machine. Only an idealised, frictionless machine could reach 100%, and even then only in principle.
How does efficiency relate to mechanical advantage?
For simple machines, η = (actual mechanical advantage ÷ ideal mechanical advantage) × 100%. Ideal mechanical advantage assumes no friction; actual mechanical advantage is measured from real force inputs and outputs, so their ratio captures the same energy loss as the work-based formula.