Radiation Pressure Calculator

Radiation pressure is the mechanical pressure exerted on a surface by electromagnetic radiation (light). Photons carry no rest mass but they do carry momentum — p = h/λ per photon, where h is Planck's constant and λ is the wavelength. When photons are absorbed, their momentum is transferred to the surface; when they reflect, the momentum reverses and twice as much is transferred. Spread over the illuminated area, that momentum flow is a pressure, measured in pascals (N/m²) just like gas pressure.

For a beam of irradiance I (W/m²) striking an opaque surface at incidence angle θ (measured from the surface normal) with reflectivity R (0 = perfectly black, 1 = perfect mirror), the normal pressure is P = (1+R)·I·cos²θ/c, where c = 299,792,458 m/s. The two textbook limits: a perfect absorber at normal incidence (R = 0, θ = 0°) gives P = I/c, and a perfect mirror (R = 1) gives P = 2I/c — reflected photons deliver twice the momentum kick.

The solar constant at 1 AU is about 1,361 W/m². Dividing by c: a perfectly absorbing surface feels P = 1,361/c = 4.5398×10⁻⁶ Pa (4.54 µPa), and a perfect mirror feels twice that, 9.0796×10⁻⁶ Pa (9.08 µPa). For scale, sea-level air pressure is 101,325 Pa — roughly 22 billion times larger. Radiation pressure is negligible on the ground but decisive in space, where there is no air drag and the tiny push acts continuously for weeks.

First find the irradiance from the isotropic inverse-square law: I = P_src/(4πr²), where P_src is the source power in watts and r the distance in metres. Then P = (1+R)·I/c. Worked example: a 100 W bulb radiating uniformly, at r = 2 m, gives I = 100/(4π×2²) = 1.9894 W/m², so a black surface feels P = 1.9894/299,792,458 = 6.6360×10⁻⁹ Pa (6.64 nPa). Use the “Source power & distance” tab — it does both steps and accepts power in W–TW or solar luminosities, distance in m, km, AU or light-years.

Thrust is pressure times area: F = P·A. Example: the LightSail 2 sail (A = 32 m², aluminized Mylar with R ≈ 0.9) in full sunlight at Earth (1,361 W/m², normal incidence) gets F = 1.9 × 1,361 × 32/c = 2.7602×10⁻⁴ N = 276.0 µN — about the weight of a grain of sand, but free and endless. A 600 m² black sail on a 100 kg craft gives a = F/m = 2.7239×10⁻⁵ m/s², which accumulates to Δv = 2.3534 m/s after one full day of sunlight. The “Solar sail” tab computes thrust, acceleration and Δv over any burn time.

Yes, through a cos²θ factor (θ measured from the surface normal). Two cosines multiply: the surface intercepts a projected area proportional to cosθ, and only the normal component of each photon's momentum (also cosθ) pushes on the surface. At 45° the pressure is exactly half the normal-incidence value; at grazing incidence it drops toward zero. Note this tool reports the normal pressure — the tangential momentum component that appears for oblique reflection is not included.

Yes — that is the photon picture. A photon of wavelength λ carries energy E = hc/λ and momentum p = h/λ. For green light at λ = 532 nm: E = 2.3305 eV per photon and p = 1.2455×10⁻²⁷ kg·m/s. If you know the photon flux Φ (photons per m² per second), the pressure is P = (1+R)·Φ·h/λ. Example: Φ = 10²¹ photons/m²/s at 532 nm on a black surface gives P = 1.2455×10⁻⁶ Pa (1.25 µPa). The “Photon flux” tab also shows each photon's energy in eV and joules.

Inside a star the radiation field is isotropic (photons come from all directions), and the pressure follows a different formula: p = 4σT⁴/(3c), where σ = 5.670374419×10⁻⁸ W/(m²·K⁴) is the Stefan–Boltzmann constant and T the local temperature. At the Sun's photosphere (5,778 K) that is only 0.281 Pa, but in the Sun's core (15.7 million K) it reaches 1.53×10¹³ Pa (15.3 TPa) — a major part of what holds the star up against gravity. The “Inside a star” tab computes it for any temperature.

Real materials sit between the textbook extremes: R = 0 (perfect absorber) and R = 1 (perfect mirror). Use R ≈ 0.9 for aluminized solar-sail film, R ≈ 0.05–0.1 for dark photovoltaic panels, and R ≈ 0.3 for typical white paint. The slider in the calculator accepts any value from 0 to 1, and the pressure scales with the factor (1+R) — so a mirror always gives exactly twice the pressure of a black surface at the same irradiance. This tool assumes the surface is opaque (nothing transmitted); transparent or translucent materials need a fuller optical model.

Scope boundary: this tool computes momentum-transfer pressure from light. It does not compute Poynting-vector energy flow (see the field energy density calculator), the slow orbital drift that solar radiation pressure causes over months (see the orbital period / orbital velocity tools), blackbody spectra or colour temperature (see the blackbody radiation and frequency-of-light tools), the inverse-square law on its own, or doses from ionizing/nuclear radiation — that is particle-flux physics, not photon momentum (see the flight radiation dose tool).