Radiation Pressure Calculator
Radiation pressure is the force per unit area that photons exert on any surface they hit. Enter a light intensity and surface type to get the pressure in pascals, the force on a chosen area, the resulting acceleration on a mass, and the velocity gain over a day. Switch to the stellar mode to compute pressure inside a star from its temperature, or use the intensity-from-star mode to work from a star's luminosity and your distance from it.
What is radiation pressure and why does it matter?
Radiation pressure is the physical force exerted by electromagnetic radiation on any surface it strikes. Although photons have no rest mass, they carry momentum: each photon has momentum p = h/lambda, where h is Planck's constant and lambda is the wavelength. When photons hit a surface, they transfer that momentum, creating a force. This force, spread over the surface area, is the radiation pressure. The effect is tiny under everyday conditions. Sunlight exerts only about 4.5 micropascals on a 1 m² patch of black material at Earth's distance from the Sun, compared to the roughly 101,325 Pa of atmospheric pressure at sea level. However, in space there is no atmosphere and no friction, so even this tiny force, sustained over days and weeks, adds up to a useful velocity change for a lightweight spacecraft. Inside massive stars, where temperatures reach millions to hundreds of millions of kelvin, radiation pressure becomes enormous and plays a fundamental role in preventing the star from collapsing under its own gravity.
The two radiation pressure formulas
This calculator covers two distinct physical situations. For external radiation pressure, where a beam of light from outside hits a surface: P = (1 + R) x I x cos²(alpha) / c Here I is the intensity in W/m², R is the surface reflectivity (0 for perfect absorber, 1 for perfect mirror), alpha is the angle between the beam and the surface normal, and c is the speed of light. The factor (1 + R) captures the extra momentum kick given to a reflective surface: an absorbing surface stops the photon (momentum = p), while a mirror reverses it (momentum change = 2p), so the mirror gets twice the push. The cos²(alpha) term accounts for the projection of the beam onto the surface and the resulting reduction in pressure when the beam strikes at an angle. For internal radiation pressure inside a star, where the photon gas is in thermal equilibrium with the plasma: P_internal = 4*sigma*T⁴ / (3*c) This comes from integrating the radiation field of a blackbody at temperature T over all directions. sigma is the Stefan-Boltzmann constant. The T⁴ dependence means pressure rises catastrophically with temperature: doubling the temperature increases internal radiation pressure sixteenfold. The intensity at a distance R from a star of luminosity L is simply I = L / (4*pi*R²), which you can feed directly into the external formula. This calculator does that automatically in the "from star" mode.
Solar sails: practical numbers
A solar sail uses radiation pressure the same way a wind sail uses air pressure, but the working fluid is sunlight instead of air. Because the force is proportional to sail area and inversely proportional to spacecraft mass, the key engineering figure of merit is the area-to-mass ratio. At 1 AU from the Sun, a perfect mirror sail delivers about 9 N per square kilometre, or 9 micronewtons per square metre. For a 600 m² sail on a 100 kg spacecraft, that is roughly 5 x 10⁻⁵ N, producing an acceleration of about 5 x 10⁻⁷ m/s². Over 30 days, this adds about 1.3 m/s. That sounds modest, but it is continuous and requires no propellant. Real sail materials such as aluminised Mylar or CP-1 polyimide have reflectivities of 0.85-0.91 and areal densities of 2-7 g/m². Including the support structure, a practical sail for an inner-solar-system mission might have a total mass of 0.1-1 kg/m². Use this calculator's area, mass, and reflectivity inputs to explore the trade-off for any proposed design. The Cosmos 1 solar sail (2005), IKAROS (2010, first successful deep-space solar sail), and LightSail 2 (2019, first controlled flight by radiation pressure alone) proved the concept at progressively larger scales. Proposed future missions include solar polar orbiters and interstellar probes using extremely thin sails and high-power laser pushing.
Radiation pressure in stellar physics
Inside a star, the temperature gradient drives photons outward, and each absorption-and-re-emission event nudges the plasma outward a tiny amount. Summed over the star's volume, this produces the radiation pressure force that opposes gravity. For the Sun, gas pressure (from thermal motion of ions and electrons) dominates radiation pressure throughout most of the interior. But for stars above about 10 solar masses, the bolometric luminosity approaches the Eddington limit, the point at which radiation pressure exactly balances gravity for hydrogen-rich material at the stellar surface. Stars cannot sustain luminosities much above this limit without blowing away their outer layers. The Eddington luminosity is L_Edd = 4*pi*G*M*c / kappa, where M is stellar mass and kappa is the opacity. For a solar-composition star this gives roughly L_Edd / L_sun = 3.2 x 10⁴ x (M / M_sun). Radiation pressure is also thought to drive the strong stellar winds from luminous blue variable stars, and it plays a central role in the spectra and light curves of Type Ia supernovae.
Radiation pressure in context
| Scenario | Intensity (W/m²) | Pressure (Pa) | Note |
|---|---|---|---|
| Sunlight at 1 AU (absorbing) | 1,361 | 4.54 × 10⁻⁶ | Solar constant, perfect absorber |
| Sunlight at 1 AU (mirror) | 1,361 | 9.08 × 10⁻⁶ | Perfect reflector, double momentum |
| Sunlight at 0.5 AU (mirror) | 5,444 | 3.63 × 10⁻⁵ | Intensity scales as 1/r² |
| Sunlight at 5 AU (absorbing) | 54.4 | 1.82 × 10⁻⁷ | Near Jupiter orbit |
| Sun photosphere (5,778 K, internal) | N/A | ~1.7 × 10⁻² | Internal, Stefan-Boltzmann formula |
| Sun corona (1,000,000 K, internal) | N/A | ~1.7 × 10⁸ | Extreme stellar plasma |
| Laser pointer (5 mW, 1 mm² beam) | 5,000 | 1.67 × 10⁻⁵ | Focused beam, absorbing target |
| High-power laser (1 MW/m²) | 1,000,000 | 3.34 × 10⁻³ | Industrial or research laser |
Representative values of radiation pressure in astrophysics and solar sail engineering.
Frequently asked questions
Why does a mirror experience more radiation pressure than a black surface?
When a photon is absorbed by a black surface, it transfers its full momentum p to the surface, where p = h/lambda = E/c (E is the photon energy). When a photon is reflected by a mirror, it reverses direction, and the change in momentum is 2p. The mirror therefore receives twice the push. This is why the formula includes the factor (1 + R): R = 0 for an absorber (factor = 1) and R = 1 for a perfect mirror (factor = 2). For a partially reflective surface with R = 0.85, the factor is 1.85, about 85% of the way from absorber to perfect mirror.
How does the incidence angle affect radiation pressure?
The incidence angle alpha is measured from the surface normal (perpendicular). At alpha = 0 degrees the beam hits face-on and the full intensity drives the pressure. At larger angles, two things reduce the pressure. First, each square metre of surface intercepts only I*cos(alpha) watts of beam power, because the beam is spread over a wider projected area. Second, the force from each absorbed or reflected photon is directed partly sideways rather than straight into the surface, reducing the normal-direction pressure component by another cos(alpha). The combined effect is a cos²(alpha) reduction. At 45 degrees the pressure is halved; at 60 degrees it is one quarter of the face-on value; at 90 degrees (grazing incidence) pressure drops to zero.
What is the solar constant, and how does intensity change with distance?
The solar constant is the intensity of sunlight at Earth's mean distance from the Sun (1 AU). Its accepted value is 1,361 W/m² (sometimes quoted as 1,360-1,362 W/m² due to the 11-year solar cycle). Because the Sun radiates equally in all directions, its light spreads over a sphere of area 4*pi*R², so intensity falls off as 1/R². At 0.5 AU (inside Mercury's orbit) the intensity is 4 x 1,361 = 5,444 W/m². At Jupiter's orbit (5.2 AU) it is about 50 W/m². Radiation pressure scales identically, so a solar sail becomes less and less effective as it moves outward from the Sun.
Can radiation pressure move large objects like asteroids?
Yes, and in fact it already does - this is called the Yarkovsky effect and the YORP effect. The Yarkovsky effect is a subtle thermal radiation pressure: one side of a rotating asteroid heats up in sunlight and then radiates that heat away as infrared photons as it rotates into shadow, giving a tiny continuous thrust. Over millions of years this can shift an asteroid's orbit enough to move it into or out of Earth-crossing trajectories. The YORP effect similarly changes an asteroid's spin rate via uneven thermal emission. NASA's DART mission (2022) used kinetic impactor deflection, but radiation pressure is a candidate for gentle, long-term orbit adjustment of hazardous asteroids.
What is the Eddington luminosity, and how is it related to radiation pressure?
The Eddington luminosity is the theoretical maximum luminosity a star can sustain without blowing itself apart. At this luminosity, the outward radiation pressure force on the stellar gas exactly balances the inward gravitational pull. For a hydrogen-rich star, L_Edd is approximately 3.2 x 10⁴ times the solar luminosity per solar mass of the star. Very massive stars like Eta Carinae radiate close to or above this limit, which drives catastrophic mass-loss events. Accreting black holes and neutron stars also encounter Eddington limits that regulate how fast they can pull in matter.
How does this calculator handle partially reflective surfaces?
Select "Partially reflective" for the surface type and enter a reflectivity R between 0 and 1. The momentum factor applied is (1 + R): a perfectly absorbing surface has R = 0 so the factor is 1; a perfect mirror has R = 1 and the factor is 2. A real aluminised Mylar sail with R = 0.88 gives a factor of 1.88, about 94% of the ideal mirror value. Any fraction of a photon that is not reflected is absorbed, contributing to heating the surface - a real engineering constraint for high-intensity applications.
Sources
- Maxwell, J.C. (1873). A Treatise on Electricity and Magnetism - foundational derivation of radiation pressure from electromagnetic theory. Oxford: Clarendon Press.
- NASA Glenn Research Center - Solar Sail Propulsion overview including force and acceleration equations.
- Carroll, B.W. and Ostlie, D.A. (2017). An Introduction to Modern Astrophysics, 2nd ed. Cambridge University Press - chapters on radiation pressure in stellar interiors and the Eddington limit.