Radiation Pressure and Solar Sail Calculator
Force, pressure and acceleration that sunlight produces on a sail at a given distance from the Sun, for any reflectivity and tilt.
Results
What this tool does
Light carries momentum, so it pushes on whatever it hits: near Earth, sunlight presses with about 4.5 micropascals on a black surface and twice that on a perfect mirror. That is tiny, but it never stops and needs no fuel. The Planetary Society's LightSail 2, a 5 kg cubesat with a 32 m² sail, demonstrated in 2019 an acceleration of a few hundredths of a millimetre per second squared, close to what this calculator gives. The push weakens with the square of the distance from the Sun and, for a tilted flat sail, with the cosine of the tilt squared; the sideways part from absorbed light is left out, and so is the sail's real curvature.
Formula
F = (1 + R) × I × A × cos²θ ÷ c · I = 1361 W/m² ÷ d²
Variables
| Symbol | Meaning | Unit |
|---|---|---|
d | Distance from the Sun | AU |
a | Sail area facing the Sun | m² |
rf | Reflectivity (0 = black, 1 = perfect mirror) | — |
m | Mass of the spacecraft | kg |
th | Tilt of the sail away from the Sun | ° |
F | Force on the sail (perpendicular) | mN |
IR | Sunlight intensity there | W/m² |
P | Light pressure | µPa |
AC | Acceleration | mm/s² |
DV | Speed gained per day | m/s |
Worked example
- Distance from the Sun1 AU
- Sail area facing the Sun32 m²
- Reflectivity (0 = black, 1 = perfect mirror)0.9
- Mass of the spacecraft5 kg
- Tilt of the sail away from the Sun0 °
- Force on the sail (perpendicular)0.2760 mN
- Sunlight intensity there1361.0 W/m²
- Light pressure8.626 µPa
- Acceleration0.0552 mm/s²
- Speed gained per day4.77 m/s
Limitations
- The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.
- The result is an estimate based only on the values you type. Real situations often include factors this calculator does not know about.