Efficiency Calculator
Efficiency tells you what fraction of the energy or power you put into a system comes back out as useful work. Solve for efficiency, output, or input by entering the other two values, switch freely between energy and power units, compare your result to the theoretical Carnot ceiling, and put a price on the energy lost as waste.
Formula
Worked example
A motor draws 1000 W and delivers 750 W of mechanical power: η = (750 ÷ 1000) × 100% = 75%. The remaining 25% (250 W) is lost as heat. Running 8 h a day for 30 days at 0.17 per kWh, that wasted 250 W costs about 10.20.
How It Works
Efficiency compares what you get out of a system to what you put in. The calculator divides the useful output by the total input and multiplies by 100 to express the result as a percentage. Because both quantities describe the same thing, energy in joules or power in watts, their units cancel and leave a pure ratio. A reading of 75% means three-quarters of the supplied energy became useful work, while the remaining quarter was lost. The calculator also reports that lost fraction directly so you can see exactly how much energy escaped as waste heat, friction, or sound.
Solving for output or input instead
You do not have to start with both output and input. Use the "Solve for" selector to rearrange the same formula three ways. Leave it on efficiency to divide output by input as usual. Switch to "useful output" to multiply a known input by a known efficiency, which tells you how much useful work a system of that quality will produce. Switch to "required input" to divide a target output by an efficiency, which tells you how much fuel or electricity you must supply to get the work you need. Each mode shows the matching show-your-work steps so the rearrangement is never a black box.
Matching and switching units
Pick energy or power as the quantity type, then choose a unit for each field independently. The output might be in kilowatt-hours while the input is in megajoules, or the output in horsepower while the input is in kilowatts. The calculator converts both to a common base (joules for energy, watts for power) before dividing, so the answer is correct even when the two fields use different units. The one rule it cannot break for you is mixing categories: you cannot divide an energy by a power, because the result would not be dimensionless. Keep both fields on the same quantity type and the ratio stays meaningful.
The Carnot ceiling and the cost of waste
For heat engines, the second law of thermodynamics sets a hard maximum called the Carnot efficiency, which depends only on the absolute temperatures of the hot and cold reservoirs: 1 minus the cold temperature divided by the hot temperature. Turn on the Carnot comparison and enter the two temperatures in kelvin, Celsius, or Fahrenheit to see that ceiling and what fraction of it your engine reaches. Separately, the cost option turns lost efficiency into money: it takes the wasted share of a power input, multiplies by your running hours and days, and prices it at your energy rate. That figure often makes the case for an upgrade clearer than the percentage alone.
What Affects the Result
Every real device loses energy along the way, and those losses set how far below 100% efficiency sits. In motors and generators, resistive heating in the windings and mechanical friction in the bearings are the main culprits. In heat engines, the Carnot limit imposes a hard ceiling that depends on operating temperatures, so even a perfect engine cannot reach 100%. Incandescent bulbs convert only a few percent of electricity to visible light, with the rest becoming heat. Improving insulation, reducing friction, and operating equipment near its design point all push efficiency higher.
Limitations
This calculator assumes you have already measured clean output and input figures; it does not derive those quantities for you, and the cost estimate treats the input as a steady power draw. Efficiency above 100% is impossible for any passive system, so a result over 100% signals a measurement or unit error rather than a remarkable machine. The figure also reflects a single operating point: efficiency often varies with load, speed, or temperature, so one measurement may not represent the whole operating range. For thermodynamic engines, compare your result against the Carnot efficiency to judge how close the design comes to the physical maximum.
Typical efficiency ranges by device
| Device or system | Typical efficiency | Rating |
|---|---|---|
| Incandescent light bulb | ~2-5% | Very low |
| Internal combustion car engine | ~20-35% | Low |
| Coal-fired power plant | ~33-40% | Low |
| LED lighting | ~40-50% | Moderate |
| Combined-cycle gas turbine | ~55-60% | Moderate |
| Electric motor (large) | ~85-95% | High |
| Lithium-ion battery (round-trip) | ~85-95% | High |
| Electric transformer | ~95-99% | Very high |
Approximate real-world efficiencies; exact values depend on design and operating conditions.
Frequently asked questions
Can I solve for the output or input instead of the efficiency?
Yes. Use the "Solve for" selector at the top. Choose "useful output" to multiply a known input by a known efficiency, or "required input" to divide a target output by an efficiency. The calculator rearranges the same formula, η = output ÷ input, and shows the working for whichever value you are solving for.
Can the output and input use different units?
Yes, as long as they are the same quantity type. Pick energy or power, then set each field independently, for example kilowatt-hours for the output and megajoules for the input. The calculator converts both to a common base (joules or watts) before dividing, so the percentage comes out right. You cannot mix an energy with a power, because the ratio would not be dimensionless.
Can efficiency ever be greater than 100%?
No. For any real, passive system efficiency must stay below 100% because some energy is always lost to heat, friction, or sound. A result above 100% means the output value exceeds the input, which violates conservation of energy, so re-check that both figures use compatible units and that you entered the useful output, not the input.
What is the Carnot efficiency, and why compare to it?
The Carnot efficiency is the maximum any heat engine can reach between two temperatures, equal to 1 minus the cold temperature divided by the hot temperature (in kelvin). No real engine beats it. Comparing your result to the Carnot limit shows how much room a design has left and separates ordinary losses from the unavoidable thermodynamic ceiling.
How is the cost of wasted energy calculated?
When the quantity type is power and the cost option is on, the calculator takes the wasted share of the input (input times the loss percentage), converts it to kilowatt-hours using your operating hours and days, and multiplies by your energy price. It is a planning figure: real bills depend on tariffs, demand charges, and how steadily the device actually runs.