Calculate efficiency increase, compare initial and final efficiency, or find final efficiency from percentage-point changes or input/output values.
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Efficiency Increase Formula
- E_initial โ starting efficiency, in percent
- E_final โ ending efficiency, in percent
- Useful output โ energy or work delivered
- Total input โ energy or work supplied
Relative increase and percentage-point change are not the same. Going from 60% to 75% is a 15 pp change but a 25% relative increase. Relative increase is undefined when the initial efficiency is zero. Output and input must use the same unit family (the calculator converts energy units to joules before dividing).
Reference Tables
Quick lookup for relative increases between two efficiency values, plus illustrative efficiency ranges. These ranges depend on equipment, operating conditions and the chosen energy basis; they are not validation limits.
| Initial โ Final | pp Change | Relative Increase |
|---|---|---|
| 50% โ 60% | +10 pp | +20.00% |
| 60% โ 75% | +15 pp | +25.00% |
| 70% โ 80% | +10 pp | +14.29% |
| 80% โ 90% | +10 pp | +12.50% |
| 85% โ 95% | +10 pp | +11.76% |
| 25% โ 40% | +15 pp | +60.00% |
| System | Typical Efficiency |
|---|---|
| Incandescent bulb | 2โ5% |
| LED bulb | 30โ50% |
| Gasoline engine | 20โ35% |
| Diesel engine | 35โ45% |
| Combined-cycle gas turbine | 55โ62% |
| Electric motor (industrial) | 85โ97% |
| Solar PV panel | 15โ22% |
| Gas furnace (condensing) | 90โ98% |
Worked Example
A pump runs at 62% efficiency. After a bearing replacement and impeller trim, it runs at 78%.
- Percentage-point change: 78 โ 62 = +16 pp
- Relative increase: 16 / 62 ร 100 = +25.81%
- Waste reduction: (38 โ 22) / 38 ร 100 = 42.11% lower wasted-energy fraction (total wasted energy depends on input energy)
FAQ
Should I report pp or percent? Use percentage points when comparing two efficiency levels directly. Use relative percent when describing improvement against a baseline.
Why is my relative increase undefined? Division by zero. If the initial efficiency is 0%, only the percentage-point change is meaningful.
Can final efficiency exceed 100%? Not for a true energy efficiency. Values above 100% usually mean you are looking at a coefficient of performance (heat pumps, chillers) or a performance ratio, not efficiency.
