Aviation & Aeronautics
Intermediate

Rate of Climb

Vertical speed from excess engine power.

Formula

ROC=excess powerWROC = \frac{\text{excess power}}{W}

Variables

powerExcess power
WWeight

Example

More power, faster climb

How it works

Rate of climb tells you how quickly an aircraft can gain altitude when it has power left over after meeting the power needed just to stay level. The excess power is the part of engine output available to do "climbing work," and dividing by weight converts that available power into a vertical speed. Because heavier aircraft need more power to gain the same height per second, the same excess power produces a lower climb rate when weight increases.

When to use it

Use this formula when estimating climb performance from engine power and aircraft weight, especially for piston aircraft or simplified performance problems. It is also useful when comparing how changes in loading, density altitude, or engine output affect climb capability.

Worked example, step by step

An aircraft has 180 kW of excess power and weighs 12,000 N. ROC = excess power / W ROC = 180,000 W / 12,000 N ROC = 15 m/s So the aircraft can climb at 15 metres per second under those conditions.

Common mistakes to avoid

  • Using total engine power instead of only the excess power
  • Forgetting to keep units consistent, such as mixing kW with N without converting to watts
  • Confusing weight with mass and plugging in kilograms directly

Did You Know?

Rate of climb is really excess power divided by weight, which is why loaded planes climb so sluggishly.

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Reviewed & maintained by the FormulaWon editorial teamLast reviewed September 2026