Multirotor hover power

Electrical hover power for a multirotor from its mass, rotors, and air density, by momentum theory with a figure of merit and motor efficiency, never the ideal power alone.

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Experimental: not yet fully verified. How results are checked

Computing your own values needs JavaScript and WebAssembly. The worked example below was computed when this page was built, and the documentation under "How we got this" applies.

150.6W

Hovering takes about 150.6 W from the battery. The ideal minimum is 76.8 W.

Ideal induced power
Total disk area
Disk loading
Air density
Power factor vs sea level

Provenance

Computed by: drone.power.hover-power 1.0.0, core 0.1.0
Model: Momentum theory: P_ideal = (m·g0)^1.5 / √(2ρA); electrical P = P_ideal / (FM·η) + avionics; ISA troposphere density
Accuracy: A first estimate. Real power depends on rotor design, frame drag, and wind; calibrate FM·η from a test flight when you can.
Notes: 1 shown with the answer
Cites: Leishman, J. G., Cambridge University Press, Principles of Helicopter Aerodynamics; International Civil Aviation Organization, Manual of the ICAO Standard Atmosphere, Doc 7488/3

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Takeoff mass Everything on board, like 1.4 kg · plain numbers mean kg Rotors Like 4 Rotor diameter Like 9.4 in · plain numbers mean in Figure of meritoptional Rotor efficiency vs ideal, 0.4 to 0.8, default 0.6

More options 5

Motor and speed-controller efficiencyoptional 0.5 to 1, default 0.85 Altitudeoptional Pressure altitude of the site, like 5000 ft; default sea level · plain numbers mean ft Air temperatureoptional Like 30 °C; default ISA for the altitude · plain numbers mean °C Density altitudeoptional Instead of altitude and temperature, like 8000 ft · plain numbers mean ft Avionics and payload poweroptional Like 10 W; default 0 · plain numbers mean W

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How we got thisFormula, worked example, sources, and proof

Model: Momentum theory: P_ideal = (m·g0)^1.5 / √(2ρA); electrical P = P_ideal / (FM·η) + avionics; ISA troposphere density

Accuracy: A first estimate. Real power depends on rotor design, frame drag, and wind; calibrate FM·η from a test flight when you can.

Worked example: A 1.4 kg quadcopter with 9.4 in rotors at sea level. Source: add-drone-suite hover scenario: disk area 0.1791 m², ideal 76.8 W, electrical 150.6 W. It is golden test vector v001, and every build checks the tool still gives its answer within its tolerance.

You enter

Takeoff mass: 1.4 kg
Rotor diameter: 9.4 in
Rotors: 4

You get

Electrical hover power: 150.6 W
Ideal induced power: 76.8 W
Total disk area: 0.1791 m²
Disk loading: 76.7 Pa
Air density: 1.225 kg/m³
Power factor vs sea level: 1

Review: Not yet independently reviewed by a Part 107 remote pilot.

Last verified: 2026-09-18, when a maintainer last confirmed this tool's sources at the issuer. See the sources ledger.

Status: version 1.0.0, core 0.1.0. See this tool in the verification report.

Checked against: 5 golden test vectors (download the test vectors, each with its source and tolerance). See how results are checked and every source.

Sources

Principles of Helicopter Aerodynamics, Leishman, J. G., Cambridge University Press, 2nd edition. Chapter 2 (momentum theory: ideal hover power T^1.5/√(2ρA), figure of merit).
Manual of the ICAO Standard Atmosphere, Doc 7488/3, International Civil Aviation Organization, 3rd edition. Troposphere equations (air density by altitude). Paid only.

Experimental means this tool has not yet met the stable bar: at least 20 golden vectors, differential tests, and an independent worked example.

Learn the concept: How to estimate drone flight time

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