Calculate reciprocating-engine indicated power or reverse-solve IMEP and RPM from bore, stroke, cylinders, cycle, pressure, and brake power with SI and US units.

Enter geometry, indicated mean effective pressure and speed.

Reciprocating-engine operating-point model. Use measured net IMEP from complete-cycle work, not gross IMEP, peak or manifold pressure. Net indicated work already includes pumping work; compare brake power at the same operating point.

Indicated Power Formula

Indicated power is the power developed inside an engine’s cylinders by the working gas acting on the pistons. Gross and net indicated power use different integration boundaries. Net indicated work includes pumping work; compare brake and indicated power on a consistent basis, including the same operating point and accessory convention. The calculator uses net IMEP from complete-cycle work; it does not convert a gross IMEP measurement into net IMEP.

IP = (100 k p L A n) / (60 s)
Symbol Meaning Common Units
IP Indicated power kW
k Number of cylinders count
p Indicated mean effective pressure (IMEP) bar, psi, kPa
L Stroke length m, cm, in, ft
A Piston area per cylinder m², cm², in², ft²
n Engine speed RPM
s Cycle factor 2 for 4-stroke, 1 for 2-stroke

In this form, pressure is in bar, L in meters, A in square meters and power in kW. The cycle factor is2 for four-stroke or1 for two-stroke. The calculator obtains piston area from bore diameter, then multiplies by stroke and cylinder count once. Mechanical hp uses745.6998715822702W.

Useful Equivalent Forms

If piston area is not already known, compute it from bore diameter first.

A = (π D²) / (4)

Displacement per cylinder is the piston area multiplied by the stroke length.

Vd = A L

That lets you write the same relationship in terms of displacement per cylinder.

IP = (100 k p Vd n) / (60 s)

If pressure is entered in pascals instead of bar, the kilowatt form becomes:

IP = (k p L A n) / (60,000 s)

How to Calculate Indicated Power

  1. Determine the number of cylinders.
  2. Measure or estimate the indicated mean effective pressure.
  3. Enter the stroke length.
  4. Enter bore diameter; the calculator computes piston area per cylinder.
  5. Enter engine speed in RPM.
  6. Select the proper engine cycle: 4-stroke or 2-stroke.
  7. Substitute the values into the formula to find indicated power.

Indicated power scales directly with cylinder count, IMEP, piston area, stroke, and speed.

IP ∝ k p A L n

Example

For a 4-cylinder, 4-stroke engine with an IMEP of 9 bar, a stroke length of 0.086 m, a bore of 0.082 m, and a speed of 3000 RPM:

A = (π (0.082)²) / (4) = 0.00528 m²
IP = (100 × 4 × 9 × 0.086 × 0.00528 × 3000) / (60 × 2) ≈ 40.9 kW

The engine develops about 40.9 kW of indicated power under those operating conditions.

Rearranged Forms for a Missing Input

If you know the target indicated power and need to solve for a different variable, these rearrangements are helpful:

p = (60 s IP) / (100 k L A n)
n = (60 s IP) / (100 k p L A)
A = (60 s IP) / (100 k p L n)
L = (60 s IP) / (100 k p A n)

Indicated Power vs. Brake Power

Indicated power is derived from cylinder work; brake power is measured shaft output. Their difference is commonly called friction power, but which pumping/accessory effects it includes depends on whether indicated work is gross or net. The efficiency task computes100 × BP/IP and rejects brake power above indicated power.

FP = IP - BP
etaₘ = (BP) / (IP)

Where:

  • FP = friction power
  • BP = brake power
  • ηm = mechanical efficiency

Practical Notes

  • Use bore diameter: cylinder count is applied once by the calculator. The formulas use area per cylinder.
  • IMEP is an average pressure: it is not the same as peak cylinder pressure.
  • Use stroke, not rod length: the stroke is the piston’s full travel from top dead center to bottom dead center.
  • Cycle selection matters: a 4-stroke engine produces one power stroke every two revolutions, while a 2-stroke produces one every revolution.
  • Keep units consistent: if one input is converted, all related dimensions should stay in matching unit systems.

Common Input Mistakes

  • Entering total displacement instead of bore diameter or stroke length.
  • Using bore radius instead of bore diameter when calculating area.
  • Forgetting to switch the cycle factor when changing from 4-stroke to 2-stroke.
  • Mixing pressure units without converting them correctly.
  • Assuming indicated power and brake power are interchangeable.