# Radiation Pressure Calculator

URL: https://speedycalculator.com/calculators/physics/radiation-pressure/
Last updated: 2026-10-30

> The radiation pressure calculator finds the pressure sunlight (or any star's light) exerts on an absorbing or reflecting surface at a given distance and angle, or the radiation pressure inside a star from its temperature.

## Inputs

- Location
- Surface
- Angle of incidence θ (°, rad, arcmin, arcsec, mrad)
- Star luminosity (L☉)
- Distance from the star (au, km, R☉)
- Temperature inside the star (K, °C, °F)
- Sail area (optional) (m², cm², mm², km², in², ft²)

## Results

- Intensity at that distance
- Radiation pressure
- Force on the sail

## Formula

```
Outside: P = (L / (4πd²c))·(1 + R)·cos²θ  (R = 0 absorbing, 1 reflecting) · Inside: P = aT⁴/3, a = 7.566 × 10⁻¹⁶ J/(m³·K⁴)
```

## Explanation

Light carries momentum, so it pushes on whatever it hits. Near Earth the push is tiny – about 9 µN per square metre for a mirror – but solar sails like IKAROS and LightSail have used it for propulsion. Inside massive stars radiation pressure helps hold them up.

### How to use the Radiation Pressure Calculator

- **Location**
- **Surface**
- **Angle of incidence θ**
- **Star luminosity (L☉)**
- **Distance from the star**
- **Temperature inside the star**
- **Sail area (optional)**

Results update as you type, every field has its own unit menu, and everything is calculated in your browser.

### How it works

Choose outside the star (surface in sunlight) or inside the star.

### Inputs explained

FieldWhat to enterLocationChoose one: Outside the star, Inside the starSurfaceChoose one: Perfectly absorbing (opaque), Perfectly reflectingAngle of incidence θUnits: °, rad, arcmin, arcsec, mradStar luminosity (L☉)A numberDistance from the starUnits: au, km, R☉Temperature inside the starUnits: K, °C, °FSail area (optional)Units: m², cm², mm², km², in², ft²

### What each result means

- **Intensity at that distance** = 3.828e26×[Star luminosity (L☉)]÷(4×pi×[Distance from the star]^2)
- **Force on the sail** = [Radiation pressure]×[Sail area (optional)]

## Worked example

Inputs — Location: Outside the star; Surface: Perfectly absorbing (opaque); Angle of incidence θ: 0 °; Star luminosity (L☉): 1; Distance from the star: 1 au; Sail area (optional): 100 m².

Results — Intensity at that distance = 1,361.16647 W/m²; **Radiation pressure = 4.54036 µPa**; Force on the sail = 454.03626 µN.

## Key terms

- **Solar sail**: A large reflective sheet propelled by light.

## FAQ

**How strong is sunlight's pressure at Earth?**
About 4.6 µPa absorbed, 9.1 µPa reflected.

**Why does a mirror get twice the push?**
Reflected light reverses its momentum.

**Can radiation pressure move spacecraft?**
Yes – solar sails use it, and it perturbs satellite orbits.

**Why is it huge inside stars?**
It grows with T⁴ and stellar cores are millions of kelvins.


## Sources

- [OpenStax – University Physics Volume 3](https://openstax.org/details/books/university-physics-volume-3)
- [NASA – Planetary fact sheet](https://nssdc.gsfc.nasa.gov/planetary/factsheet/)