The radiation pressure calculator above turns a light intensity into a mechanical pressure. Electromagnetic radiation carries momentum as well as energy, so when light lands on a surface it pushes. The push is minute by everyday standards and completely inescapable, which makes it negligible in a room and decisive in spaceflight, in stellar structure and in optical trapping.
Arb Digital publishes free physics calculators that each own one relation properly. This page handles the momentum side of light. The photon energy calculator handles the energy side, converting wavelength into energy per photon, and the inverse square law calculator gives you the intensity at a distance that this page then takes as its input.
What This Radiation Pressure Calculator Does
Give it an intensity in watts per square metre and it returns the pressure on a perfect absorber, the pressure on a perfect mirror, and the pressure on a surface with the reflectivity you specify, which sits between the two. Add an area and it gives the total force; add a mass and it gives the acceleration.
The default intensity is 1,361 W/m², which is close to the total solar irradiance at one astronomical unit. The default area and mass describe a small solar sail: a thousand square metres of highly reflective film on a ten-kilogram spacecraft. Those numbers make the point better than any explanation, because the force comes out in millinewtons and the resulting velocity change over a few months is substantial.
An angle of incidence input is provided because the geometry matters in practice. Light arriving off-normal spreads over more area and its reflected momentum no longer points straight back, so the useful force falls faster than the cosine of the angle alone.
How to Use It
- Enter the intensity at the surface. For sunlight in space that is the solar constant scaled by the inverse square of distance; for a laboratory beam it is power divided by spot area.
- Set the reflectivity. Use 0 for a black absorber, 1 for an ideal mirror, and something in between for a real film.
- Enter the projected area. This is the area the beam actually sees, which for a tilted surface is smaller than the physical area.
- Add a mass for the acceleration. This is what turns a pressure into something you can integrate over a mission.
- Adjust the angle if the surface is tilted. Sail steering works precisely by tilting, so this is not a detail.
The Formula: How Radiation Pressure Is Calculated
For a perfectly absorbing surface at normal incidence, the time-averaged radiation pressure is p = I ÷ c, where I is the intensity and c is the speed of light. For a perfectly reflecting surface it doubles to p = 2I ÷ c, because the photon momentum is reversed rather than merely stopped. OpenStax University Physics, Volume 2, section 16.4 on momentum and radiation pressure derives both results from the energy density of the wave and gives the time-averaged forms in terms of intensity directly.
A real surface with reflectivity R lies between them: p = (1 + R)I ÷ c. Force is that pressure multiplied by the projected area, and acceleration is force divided by mass. At an angle θ from the normal, the absorbed component contributes cosθ from the reduced projected area while the specularly reflected component contributes a further cos²θ along the beam direction, so the axial force scales as (1 + R cos²θ) cosθ relative to the normal-incidence absorber value.
For the intensity default, NASA's Solar Radiation and Climate Experiment fact sheet gives roughly 1,368 watts per square metre of solar energy illuminating the outermost atmosphere on average; modern satellite composites centre a little lower, near 1,361, which is the value used here as a default. The application that makes all of this practical is described on NASA's Advanced Composite Solar Sail System mission page, which states plainly that solar sails employ the pressure of sunlight for propulsion and so carry no propellant.
Work the defaults by hand. At I = 1,361 W/m², the absorber pressure is 1,361 ÷ 299,792,458 = 4.540 × 10−6 Pa, and a perfect mirror would see 9.080 × 10−6 Pa. With R = 0.9 the pressure is 1.9 × 4.540 × 10−6 = 8.626 × 10−6 Pa. Over 1,000 m² that is a force of 8.626 × 10−3 N, and on a 10 kg spacecraft an acceleration of 8.626 × 10−4 m/s². Sustained, that reaches 1 km/s in about 1.16 million seconds — roughly thirteen and a half days.
Why a Mirror Feels Twice the Push
The factor of two is momentum conservation, not an optical curiosity. A photon carrying momentum p that is absorbed delivers p to the surface. A photon that reflects straight back arrives with +p and leaves with −p, so the surface receives 2p. Double the momentum transfer, double the pressure, for exactly the same energy arriving.
This has a consequence people find counterintuitive. A black sail and a mirrored sail of the same area absorb and receive the same energy, but the mirror gets twice the thrust. The black one also heats up and re-radiates, which produces a small additional recoil, but re-emission is roughly isotropic and so mostly cancels.
The same logic explains the reflectivity term. A film that reflects 90 per cent of the incident light returns 90 per cent of the momentum and absorbs the rest, giving a factor of 1.9 rather than 2. That 5 per cent shortfall against an ideal mirror is why sail films chase reflectivity so hard.
Where Radiation Pressure Actually Matters
In stars it is structural. In massive stars the outward radiation pressure is a significant fraction of the support against gravity, and above the Eddington limit it exceeds gravity entirely and drives mass off the surface. The stellar luminosity calculator works the output side of that, and the blackbody radiation calculator the emission spectrum.
In the solar system it shapes small bodies. Comet dust tails point away from the Sun because radiation pressure on micron-scale grains overcomes solar gravity, while the heavier grains that make up the antitail do not. The Poynting-Robertson effect, a subtler relativistic consequence, slowly spirals small dust grains inward over long timescales.
In spacecraft operations it is a routine perturbation, not an exotic one. Solar radiation pressure on large solar arrays and antennas has to be modelled in precision orbit determination for geostationary satellites and navigation constellations; ignoring it produces position errors that accumulate. And in the laboratory it is a tool: optical tweezers hold and move micron-sized particles using the gradient force of a focused laser beam.
Reading the Numbers Honestly
Micropascals are easy to underestimate. Full sunlight on a mirror is about nine micropascals, roughly one ten-billionth of atmospheric pressure. On a one-square-metre mirror that is nine micronewtons, comfortably less than the weight of a grain of sand. No experiment you can do at a kitchen table will show it, and the Crookes radiometer that appears to demonstrate it is actually driven by residual gas, not by light pressure at all.
What changes the picture is time and mass. There is no propellant to run out of, so a small acceleration integrates without limit. The figure that matters for a sail is characteristic acceleration — force divided by total spacecraft mass — and it is driven by areal density, the mass per square metre of the whole vehicle including structure. That is why sail engineering is a materials problem far more than a physics problem.
For the trajectory side of the same question, the Hohmann transfer calculator covers the impulsive-manoeuvre alternative and the rocket thrust calculator the propellant-based case that a sail is trying to avoid.
Arb Digital builds free tools like this one because useful pages earn attention. If you want tools, calculators or content built for your own audience, we can help.
Browse All Free Tools Talk to Arb DigitalCommon Mistakes to Avoid
- Using energy instead of momentum — pressure is intensity divided by the speed of light, not intensity itself. The factor of c is what makes the number so small.
- Forgetting the factor of two for a mirror — reflection reverses momentum, so it transfers twice as much as absorption for the same energy.
- Using total surface area rather than projected area — only the area the beam actually intercepts contributes.
- Assuming intensity is constant with distance — solar intensity falls as the inverse square, so a sail at 2 AU has one quarter the pressure it had at 1 AU.
- Citing the Crookes radiometer as a demonstration — it spins the wrong way for radiation pressure and is driven by thermal transpiration in the residual gas.
Related Free Tools From Arb Digital
Get the intensity at your distance from the inverse square law calculator, and the per-photon energy from the photon energy calculator. For stars, use the stellar luminosity calculator and the blackbody radiation calculator. On the mechanics side, the momentum calculator covers ordinary momentum transfer and the escape velocity calculator the gravity you are working against. For mission design compare the Hohmann transfer calculator and the rocket thrust calculator. Terrestrial solar output is covered by the solar panel calculator. Everything Arb Digital publishes is listed on the free online tools hub.
Frequently Asked Questions
It is the mechanical pressure light exerts on a surface, because electromagnetic radiation carries momentum as well as energy. For a perfect absorber it equals the intensity divided by the speed of light, and for a perfect mirror it is twice that.
Because reflection reverses the photon momentum rather than simply stopping it. An absorbed photon delivers its momentum once; a reflected one arrives with momentum in one direction and leaves with it reversed, so the surface receives twice as much.
At about 1,361 watts per square metre, a perfect absorber sees roughly 4.5 micropascals and a perfect mirror about 9.1 micropascals. That is around one ten-billionth of atmospheric pressure, which is why it is undetectable in everyday life.
Because it never stops and costs no propellant. A small acceleration applied continuously for months builds a large velocity change, so what matters is the spacecraft's areal density rather than the instantaneous force.
Yes, in two ways. Tilting reduces the projected area the beam intercepts, and the reflected momentum no longer points straight back along the beam. The axial force therefore falls faster with angle than the projected area alone would suggest.
No. It spins in the direction opposite to what radiation pressure would produce. The motion is driven by thermal transpiration in the residual gas around the unevenly heated vanes, not by light pressure.
Yes. Solar radiation pressure on large arrays and antennas is a standard perturbation in precision orbit determination, particularly for geostationary and navigation satellites, where neglecting it produces position errors that accumulate over time.
This tool is provided for educational and study use. It evaluates the published time-averaged radiation pressure relations for ideal absorbing and specularly reflecting surfaces, and does not model diffuse scattering, thermal re-emission, spectral variation, absorption heating or the Poynting-Robertson effect. Treat its output as a physics result rather than a mission-design value.
