Radiation Pressure Calculator - Light Force on Absorbers and Mirrors

A radiation pressure calculator turns any light intensity into the pressure a beam exerts on a surface and the total force it delivers to a chosen area. The physics is the same for sunlight on a solar sail, a laser on a micromechanical mirror, or a blackbody source in vacuum: P_rad = (I/c) * (1 + R) * cos^2(theta), with the speed of light in the medium replacing c when light travels through water or glass.

• • Solar sail sizing: Read the force on a 100 m^2 perfectly reflecting sail at the Earth's solar constant (about 9.08e-4 N) before committing to a deployable membrane.
• • Optical trap force: Estimate the radiation pressure from a tightly focused laser in optical tweezers, where forces are in the piconewton range.
• • Radiometer calibration: Compare predicted radiation pressure on the black and mirrored vanes of a Crookes radiometer to expected vane motion.
• • Laser ablation recoil: Compute the reaction force when a high-power laser deposits momentum, used in laser propulsion and pulsed laser deposition.

Defaults are sunlight at Earth's orbit (1361 W/m^2) hitting a perfect mirror at perpendicular incidence, so the calculator reads the textbook solar sail number on first load. Switching reflectivity to 0 halves the result for an absorber; setting the angle to 45 degrees quarters it through cos^2(theta).

When the light source is a thermal radiator rather than a laser, the Blackbody Radiation Calculator provides the spectral exitance and peak wavelength that feeds back into the intensity used here.

The calculator reads intensity, reflectivity, angle, medium refractive index, and target area, converts the angle into radians, divides the vacuum speed of light by n to get c_medium, then evaluates P_rad = (I / c_medium) * (1 + R) * cos^2(theta) and F = P_rad * A.

• I: Light intensity in watts per square meter (W/m^2). For a laser, I equals beam power divided by beam area.
• R: Surface reflectivity between 0 (perfect absorber) and 1 (perfect mirror).
• theta: Angle of incidence between the incoming light and the surface normal in degrees. 0 is perpendicular, 90 is grazing.
• n: Refractive index of the medium. Vacuum and air use 1.000; water uses about 1.333.
• A: Target surface area in square meters used for the total force output.

The factor (1 + R) covers both perfect absorption (R = 0, giving the textbook I/c) and perfect reflection (R = 1, doubling the result), and handles partial reflectivity from anti-reflection coatings. The cos^2(theta) factor combines two effects: the projected area shrinks as cos(theta) and the normal-component of momentum transfer shrinks as cos(theta), multiplying together. Inside a medium the speed of light drops to c/n, raising the pressure by n for the same intensity.

According to NIST CODATA speed of light, the speed of light in vacuum is exactly 299,792,458 m/s by the SI definition of the metre, the constant used as the denominator of every radiation pressure result in vacuum.

When the beam is so intense that individual photon recoils matter, the Compton Wavelength Calculator provides the photon momentum change on a single electron that underlies the (1 + R) factor in this formula.

Four ideas hold the calculator together: photon momentum, the intensity-pressure link, the role of reflectivity, and the medium refractive index.

These four ideas drive the Poynting vector, the radiation reaction force on accelerating charges, and the Crookes radiometer mechanism. According to Wikipedia - Radiation Pressure, the pressure inside a transparent medium scales as (I/c_medium) and the angle correction still uses cos^2(theta) once refraction is accounted for, which is why this calculator accepts the medium refractive index.

The (1 + R) factor is exactly the conservation of momentum applied to a photon bouncing off a mirror, which is the same setup the Conservation of Momentum Calculator solves for any pair of colliding masses.

Pick an intensity, set the reflectivity and angle to match your surface, choose the medium, then read the radiation pressure, total force, and pressure-vs-atmosphere from the results panel.

1. 1 Enter the light intensity: W/m^2. Default 1361 is the solar constant at Earth's orbit. For a laser, intensity equals beam power divided by beam area.
2. 2 Set the surface reflectivity: 0 for a perfect absorber (soot, matte black paint), 1 for a perfect mirror, anything in between for a partial reflector.
3. 3 Choose the angle of incidence: 0 degrees means perpendicular; 90 is grazing. Pressure scales as cos^2 of this angle.
4. 4 Pick the medium: 1.000 for vacuum and air, 1.333 for water, about 1.5 for typical glass. Higher index raises the pressure for the same intensity.
5. 5 Enter the target area: Square meters the light hits. Solar sails use 10 to 1000 m^2; optical tweezers trap cells in regions of about 1e-9 m^2.
6. 6 Read the pressure and force: Headline output is pressure in Pa. Force and momentum flux follow; pressure-vs-atmosphere shows how small radiation pressure is compared to air.

For a 100 m^2 perfectly reflecting solar sail at Earth's orbit, keep the defaults (1361 W/m^2, R = 1, theta = 0, n = 1, A = 100); the result reads about 9.08e-4 N, the force that must be balanced against solar gravity to maintain attitude.

When the light source is pulsed or modulated, the Harmonic Wave Equation Calculator reads the frequency and wavelength of the envelope so the average intensity can be tracked over each pulse.

The radiation pressure calculator combines photon momentum, intensity scaling, reflectivity, and medium refractive index into one panel so coursework, lab checks, and solar sail design share the same numbers.

• • Four physical inputs, one panel: Intensity, reflectivity, angle, and refractive index feed the formula; area is a separate input because it scales force but not pressure.
• • Vacuum and non-vacuum media: Switch between vacuum, air, water, glass, and any custom refractive index the experiment requires.
• • Reference comparisons built in: The pressure-versus-atmosphere field shows radiation pressure as parts per million of atmospheric pressure, a sanity check that radiation forces are tiny compared to air.
• • Continuous reflectivity input: Reflectivity is a continuous 0-to-1 number, so partial reflectors, anti-reflection coatings, and absorbing substrates all fit the same formula.
• • Worked example baked in: Defaults match sunlight on a perfect mirror at Earth's orbit and the worked example reproduces the solar sail force to better than 1%.

If the question shifts to a single photon recoil on an electron, the same Planck constant and speed of light drive the neighboring calculators in this category.

Three input factors change every output, with the medium refractive index as a fourth caveat. The limits below describe where the closed-form model is reliable and where it stops being exact.

• • The model assumes a collimated beam of uniform intensity; real laser beams have a Gaussian profile and real sunlight is not perfectly collimated.
• • Inside a medium at oblique incidence the angle used in cos^2(theta) must be the refracted angle inside that medium, not the external angle of incidence.
• • Very high intensities (gigawatt per square meter and above) drive nonlinear effects such as self-focusing and ionization that the closed-form P_rad = I/c relation does not capture.
• • The calculator reports force on a stationary surface only; it does not include recoil on the light source itself or radiation reaction.

Radiation pressure is much smaller than atmospheric pressure: at the solar constant on a perfect mirror, P_rad is roughly 9e-6 Pa compared to 101325 Pa of air, about 0.09 parts per million. That is why a Crookes radiometer works best in a partial vacuum: residual gas drag dominates the visible motion at standard pressure, and the light-driven side takes over only when air is pumped out.

According to Wikipedia - Solar sail, the radiation pressure on a perfectly reflecting surface is exactly twice that of a perfect absorber (P_rad = 2I/c at perpendicular incidence), and this doubled force is the basis for every solar sail design from the Planetary Society's LightSail to proposed interstellar probes.

For thermal light sources rather than a single laser line, the Boltzmann Factor Calculator computes the photon occupation of each wavelength so the average intensity across a blackbody spectrum can be folded into this calculator.