Radiation Pressure Calculator
Calculate the pressure and force that light exerts on a surface, from a solar sail at a chosen distance from the Sun or from a direct flux value.
☀️ What is Radiation Pressure?
Radiation pressure is the mechanical pressure that electromagnetic radiation, including ordinary light, exerts on any surface it strikes. Although photons are massless, they carry momentum proportional to their energy, and when large numbers of them hit a surface every second, that momentum transfer produces a small but measurable force per unit area. James Clerk Maxwell predicted the effect theoretically in the 1860s from his electromagnetic theory, and it was confirmed experimentally around 1900 by Pyotr Lebedev and separately by Ernest Nichols and Gordon Hull.
This calculator has three main uses: estimating the force on solar sail spacecraft that use sunlight for propulsion, modeling laser-propulsion concepts such as Breakthrough Starshot which use powerful directed lasers instead of sunlight, and teaching the physics of how flux, reflectivity, and area combine to produce a usable thrust from something as seemingly insubstantial as light. Enter either a distance from the Sun (using the well-established inverse-square law for solar flux) or a direct flux value for a non-solar light source.
A common misconception is that radiation pressure is negligible and therefore irrelevant. While the pressure itself is genuinely tiny, a few micropascals from sunlight near Earth, it acts continuously and without any propellant mass penalty, which makes it uniquely valuable for very long-duration missions. Another misconception is that absorbing and reflecting surfaces feel the same pressure, when in fact a perfectly reflecting surface feels exactly twice the pressure of a perfectly absorbing one for the same incoming flux, because reflected photons transfer twice the momentum of absorbed ones.
This calculator is useful for aerospace students studying propellant-free propulsion, science communicators explaining solar sail missions like IKAROS, LightSail 2, and NASA's proposed interstellar concepts, and anyone curious how much force sunlight or a laser beam could realistically exert on a spacecraft of a given size.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 — Reflecting Solar Sail at 1 AU
Distance = 1 AU, Area = 1,000 m², Reflectivity = 1 (fully reflecting, like a mirrored sail)
Example 2 — Absorbing (Black) Sail at 1 AU
Distance = 1 AU, Area = 1,000 m², Reflectivity = 0 (fully absorbing, like a black panel)
Example 3 — Laser-Propelled Lightsail (Direct Flux Mode)
Direct flux = 100,000 W/m² (a concentrated laser beam), Area = 10 m², Reflectivity = 1
❓ Frequently Asked Questions
🔗 Related Calculators
What is radiation pressure?
Radiation pressure is the physical pressure exerted on a surface by electromagnetic radiation, including visible light. Photons carry momentum even though they are massless, and when they strike, and especially when they reflect off, a surface, that momentum transfers to the surface as a tiny but real force per unit area.
What is the formula for radiation pressure?
For a perfectly absorbing surface, pressure P equals I divided by c, where I is the radiant flux (power per unit area, in watts per square meter) and c is the speed of light. For a perfectly reflecting surface, the pressure doubles to P equals 2I over c, because reflected photons reverse direction and transfer twice the momentum of absorbed ones.
Why does a reflecting surface feel twice the pressure of an absorbing one?
Momentum transfer depends on the change in the photon's momentum. An absorbed photon's momentum goes entirely into the surface (a change of p). A reflected photon leaves with momentum reversed (a change of 2p), so it delivers twice the momentum kick per photon, doubling the pressure for the same incoming flux.
What is the solar constant and how does the calculator use it?
The solar constant is the solar radiant flux measured at 1 astronomical unit from the Sun, about 1361 watts per square meter. In Distance mode, the calculator derives flux at any chosen distance using the inverse-square law, I(d) equals the Sun's total luminosity divided by 4 pi d squared, which reduces to the solar constant at exactly 1 AU.
How is force on a solar sail calculated?
Force equals pressure multiplied by the sail's area, F = P times A. Since pressure from sunlight is only a few micropascals near Earth, meaningful thrust requires a large sail area, real proposed and flown solar sails range from tens to thousands of square meters.
What does the reflectivity slider represent?
The reflectivity slider interpolates continuously between a perfectly absorbing surface (0, black, P = I/c) and a perfectly reflecting surface (1, mirror-like, P = 2I/c) using P = (I/c)(1+r). Real materials fall somewhere in between, absorbing part of the incident light and reflecting the rest.
When should I use Flux mode instead of Distance mode?
Use Flux mode when the light source is not the Sun at a known AU distance, for example a laser-propulsion concept like Breakthrough Starshot, a spacecraft near a different star, or any scenario where you already know the radiant flux in watts per square meter directly, rather than deriving it from solar distance.
How much force does sunlight exert on a real solar sail?
A 1,000 square meter fully reflecting sail at 1 AU experiences roughly 9 millinewtons of force, a tiny push by everyday standards, but sustained continuously and acting on a low-mass spacecraft in the vacuum of space, it can produce meaningful acceleration and delta-v over months to years without consuming any propellant.
Does radiation pressure only come from the Sun?
No. Any source of electromagnetic radiation exerts radiation pressure, starlight, laser beams, and even the cosmic microwave background all contribute a (usually far smaller) pressure. Laser-based propulsion concepts intentionally use concentrated, powerful beams to achieve much higher flux, and therefore much higher pressure, than sunlight alone provides.
Why is radiation pressure measured in micropascals for typical sunlight?
A pascal is 1 newton per square meter, an already small unit, and sunlight's pressure at Earth's distance is only a few millionths of a pascal (micropascals). This calculator displays pressure in micropascals so the numbers are readable, alongside force in millinewtons and newtons, which scale with the sail's total area.
How does distance from the Sun affect radiation pressure?
Radiation pressure follows the inverse-square law just like flux, doubling the distance from the Sun quarters the pressure, and moving to Jupiter's distance (about 5.2 AU) reduces the pressure to roughly 1/27th of its value at Earth's distance (1 AU), since 5.2 squared is about 27.