Set your target speed, available thrust and motor RPM — get diameter, pitch and a feasibility check, recomputed as you type.
Leave at 0 to skip the prop-efficiency estimate.
Preliminary static-C_T model. Need wing loading, stall/AoA, moment or full trim analysis too? The rest of the suite is still available in the full calculator app while it's converted over one dashboard at a time.
Two independent relations run this page — one sets diameter from thrust, the other sets pitch from speed — then a few dimensionless ratios check whether the result is sane.
A propeller's static thrust follows the thrust-coefficient relation from momentum theory, where n is the shaft speed in revolutions per second (RPM / 60), ρ is air density and C_T is a non-dimensional thrust coefficient (≈0.08–0.15 for a typical multirotor prop):
Rearranged for the diameter needed to hit a required thrust:
Because thrust scales with D⁴, small diameter changes move thrust a lot — and because hover power (see the battery calculator's physics tab) falls with disc area, a bigger, slower prop is almost always more efficient than a smaller, faster one producing the same thrust.
Pitch is the distance the prop would advance in one revolution if it behaved like a screw with no slip. At n rev/s, the no-slip ("pitch") speed it's built for is:
Real props always slip — the actual cruise speed sits below the pitch speed by the slip fraction. Solving for the pitch that puts your wanted speed at the right slip margin:
As forward speed approaches the pitch speed, the blade's local angle of attack collapses toward zero and thrust falls with it — the chart above approximates that falloff linearly from the static value down to zero exactly at V_pitch. The wanted speed (green) has to stay clear of the pitch speed (red), or there's no thrust margin left to overcome drag.
Two dimensionless numbers describe the operating point regardless of absolute size, useful for comparing against known-good propellers:
P/D ≈ 0.3–0.8 covers efficient "cruise" props; above 1.0 is an aggressive high-pitch "speed" prop. P/D and J are related by P/D = J / (1 − slip).
The blade tips move far faster than the vehicle — fast enough to approach the speed of sound on a small, high-RPM prop. Compressibility drag and noise both rise sharply above tip Mach ≈ 0.7:
This is why very high RPM forces a smaller diameter (to keep the tip under Mach 0.7), and why big, slow propellers are both quieter and more efficient. This is a preliminary static-C_T model — for final design, replace C_T with a measured prop map or blade-element/CFD data.