Radiation Pressure Calculator

Introduction

Radiation pressure is the mechanical pressure produced when electromagnetic radiation transfers momentum to a surface. A dark absorber receives the incoming photon momentum. A nearly ideal mirror receives a larger push because the photon direction reverses, doubling the momentum change for normal incidence. The effect is tiny in everyday units, but it matters in solar sails, optical cavities, high-power lasers, dust dynamics, and very luminous astrophysical systems.

This calculator estimates radiation pressure from light intensity and reflectivity, then converts that pressure into force, acceleration, and one-day delta-v for a flat surface. It is an order-of-magnitude physics tool, not a full optical, thermal, or spacecraft-dynamics model.

How to use this calculator

Enter the radiant intensity in watts per square meter, the reflectivity from 0 to 1, the illuminated surface area, the incidence angle, and the accelerated mass. Use an incidence angle of 0 degrees when the beam travels along the surface normal. Use higher angles for a tilted sail or mirror; in this simplified model the normal pressure scales with cos²(θ).

The default intensity is close to sunlight near Earth orbit, and the default reflectivity approximates a bright sail. If you are modeling a laser spot, use the beam power divided by illuminated area as the intensity. If the mass is unknown, leave the default as a placeholder and focus on pressure and force.

Formula and method

For normal incidence on a flat surface, this calculator uses

where P is pressure in pascals, I is intensity in W/m², R is reflectivity, and c = 299,792,458 m/s is the speed of light in vacuum. For an absorbing surface, R = 0 and P = I / c. For an ideal mirror, R = 1 and P = 2I / c.

For a tilted flat surface, the normal pressure is reduced here by cos²(θ), where θ is the angle between the incoming beam and the surface normal. The force is then F = P A, acceleration is a = F / m, and one-day delta-v is a multiplied by 86,400 seconds.

Example calculation

At Earth orbit, sunlight is roughly 1,361 W/m² before atmospheric losses. A 100 m² sail with reflectivity 0.9 and face-on illumination has pressure about 8.63 micro-pascals. Multiplying by 100 m² gives a force of about 0.000863 newtons. If the sailcraft mass is 10 kg, the acceleration is about 0.0000863 m/s², which is roughly 7.46 m/s of idealized delta-v per day.

Those numbers are small compared with rocket thrust, but they accumulate continuously without propellant. That is why radiation pressure can matter for precise spacecraft navigation and for lightweight solar-sail missions.

How to interpret the result

Most radiation-pressure values are far below everyday mechanical pressures. Atmospheric pressure at sea level is about 101,325 Pa, while sunlight on a sail is usually in the micro-pascal range. The force becomes useful when the illuminated area is large, the mass is low, and drag is negligible.

Reflectivity and angle are the most important surface controls. Higher reflectivity increases momentum transfer, while a more grazing incidence reduces the normal push. For laser systems, intensity can become the dominant driver, but thermal damage, material deformation, and safety limits often matter before radiation pressure alone becomes large.

Limitations and assumptions

• Flat uniform surface. The calculation assumes a single flat area with uniform intensity and one reflectivity value.
• Simple specular reflection. Diffuse scattering, absorption spectra, polarization, wavelength dependence, and multilayer optical coatings are not modeled.
• Vacuum speed of light. The formula ignores refraction, absorption, scattering, plasma effects, and atmospheric drag.
• No thermal or structural response. Heating, wrinkling, sail billow, damage thresholds, and shape control can dominate real designs.
• No orbital mechanics. The delta-v output assumes constant acceleration in one direction for a day. Real trajectories require vector dynamics and attitude control.
• Educational estimate only. Do not use this as the sole basis for safety-critical optical, laser, or spacecraft engineering decisions.

FAQ

Why does a mirror feel more radiation pressure than an absorber?

An absorbing surface takes in photon momentum once. A mirror reverses the photon direction, so the momentum change is roughly doubled for ideal normal reflection.

Does the incidence angle matter?

Yes. For a flat surface, the normal pressure falls with the square of the cosine of the angle between the beam and the surface normal in this simplified model. A tilted sail may still use transverse components for steering, but that requires vector analysis.

Can this calculator design a real solar sail?

No. Real sail design also needs attitude dynamics, reflectance spectra, wrinkles, thermal limits, degradation, mass distribution, deployment constraints, and orbital mechanics.