Library / Fundamentals / FUN-04
Fundamentals
Efficiency
Fraction of input power that becomes useful output.
- Ref
- FUN-04
- Rev
- v1
- Field
- Fundamentals
- Result
- η [%]
η is dimensionless and shown here as a percentage. Compare input and useful output power over the same operating interval.
Efficiency is the part of the power you put in that comes out as something useful. The rest is lost, usually as heat.
Calculator
- Power lost3.6 kW
- Losses as a share of input30 %
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- Efficiencies multiply along a chain: a motor at 90% driving a gearbox at 95% gives about 85.5% overall.
- Losses become heat that must be removed, so a few per cent of efficiency can decide the cooling design.
- No real machine can reach or exceed 100%.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (%) | Local step | Change in result |
|---|---|---|---|---|---|---|
| Pin Input power | 5 to 80 kW | 10.5 | 96.49 | 85.99 | +10% | −6.36 pp |
| Puseful Useful output power | 2 to 40 kW | 16.67 | 91.01 | 74.35 | +10% | +7 pp |
Sweep of Input power
| Input power (kW) | Efficiency (%) |
|---|---|
| 5 | — |
| 7.071 | — |
| 10 | 84 |
| 14.14 | 59.4 |
| 20 | 42 |
| 28.28 | 29.7 |
| 40 | 21 |
| 56.57 | 14.85 |
| 80 | 10.5 |
Sweep one variable
Variables and how each one contributes
Efficiency
What the equation gives you. Everything else feeds it.
Useful output power
Power delivered to the intended job. Directly proportional at fixed input: more useful output means higher efficiency.
Input power
Power supplied to the machine. Inversely proportional: for the same output, a larger input means lower efficiency.
Worked example with the values above
- Both powers are in kW, so the ratio is dimensionless.
- η = 8.4 / 12 = 0.7.
- As a percentage the efficiency is 70 %, so 3.6 kW is lost.
Assumptions and limits
- Input and output measured over the same interval and at steady conditions.
- Same kind of quantity in both (both power, or both energy).
- One operating point; efficiency usually varies with load.
Common mistakes
- Comparing powers at different loads or times.
- Using the efficiency of one stage as the whole system.
- Forgetting the answer is a fraction, not a percentage, when multiplying chains.
Statistics and uncertainty
For a ratio, relative errors combine as δη/η ≈ √[(δPu/Pu)² + (δPin/Pin)²]. Two instruments with 2% error each give roughly 2.8% on η, which on an 85% efficiency is about ±2.4 percentage points.
Where it is used
- Rating motors, engines, pumps and generators.
- Battery-to-wheel energy budgets.
- Deciding how much cooling a machine needs.
Maths you need
- Ratios and percentages: η is a ratio shown as a percentage
- Power: both terms are powers in the same unit