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
Relative increase (%) = (E_final - E_initial) / E_initial * 100
Percentage-point change (pp) = E_final - E_initial
E = Useful output / Total input * 100
- E_initial — starting efficiency, in percent
- E_final — ending efficiency, in percent
- Useful output — energy or work delivered
- Total input — 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 typical efficiency ranges to sanity-check your inputs.
| Initial → Final | pp Change | Relative Increase |
|---|---|---|
| 50% → 60% | +10 pp | +20.00% |
| 60% → 75% | +15 pp | +25.00% |
| 70% → 80% | +10 pp | +14.29% |
| 80% → 90% | +10 pp | +12.50% |
| 85% → 95% | +10 pp | +11.76% |
| 25% → 40% | +15 pp | +60.00% |
| System | Typical Efficiency |
|---|---|
| Incandescent bulb | 2–5% |
| LED bulb | 30–50% |
| Gasoline engine | 20–35% |
| Diesel engine | 35–45% |
| Combined-cycle gas turbine | 55–62% |
| Electric motor (industrial) | 85–97% |
| Solar PV panel | 15–22% |
| Gas furnace (condensing) | 90–98% |
Worked Example
A pump runs at 62% efficiency. After a bearing replacement and impeller trim, it runs at 78%.
- Percentage-point change: 78 − 62 = +16 pp
- Relative increase: 16 / 62 × 100 = +25.81%
- Waste reduction: (38 − 22) / 38 × 100 = 42.11% less wasted 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.
