Radiation Pressure Calculator

Calculate radiation pressure, photon momentum, and force exerted by electromagnetic radiation.

Solar constant: 1370 W/m²
0=absorber, 1=mirror
Please check your inputs and try again.

Light Carries Momentum as Well as Energy

Electromagnetic radiation exerts pressure because it transports momentum and transfers that momentum when absorbed or reflected. For normally incident light that is completely absorbed, radiation pressure is p=I/c. For ideal reflection back along the incident direction, the momentum change doubles and p=2I/c. Multiplying pressure by illuminated area gives force.

For an individual photon, momentum is pγ=E/c=h/λ. Radiation pressure is usually tiny in everyday conditions, but it matters in high-power lasers, stellar environments, optical trapping, and solar-sail concepts because it acts continuously without requiring material contact.

Absorbed: p=I/c;   reflected: p=2I/c;   photon momentum pγ=h/λ
SymbolMeaningWhy it appears / units
IRadiant intensityW/m²; energy flux incident on the surface.
pRadiation pressurePa=N/m².
AIlluminated aream²; force F=pA for uniform pressure.
λPhoton wavelengthm; shorter wavelength means greater momentum per photon at fixed photon count.

Reflection produces about twice the normal momentum transfer of perfect absorption because photon momentum reverses direction. Partial reflectivity and non-normal incidence require resolving momentum components and accounting for absorbed, reflected, and transmitted fractions.

Radiation pressure should scale linearly with intensity. Doubling optical intensity doubles force on the same area. The reflecting case should be twice the absorbing case at normal incidence; if those limits are reversed, inspect the momentum-change factor rather than the speed-of-light conversion.

Worked Examples

Example 1: Solar sail 1AU: I=1370 W/m², A=100m², r=0.9 mirror
P=1370×1.9/(3e8)
Result: F=8.68×10⁻⁶ N per 100m²
Tiny force but constant — builds up over months
Example 2: High-power laser: I=10¹⁰ W/m², A=1cm²
P=10¹⁰/3e8 on absorber
Result: F=3.33×10⁻⁴ N — measurable!
Optical tweezers use radiation pressure to trap cells
Example 3: Sunlight on absorbing surface
I=1000W/m²
Result: p=3.34μPa
Radiation pressure is very small despite substantial solar power per square meter.
Example 4: Perfect mirror, 20m²
I=1000W/m², A=20m²
Result: F≈0.134mN
Perfect reflection doubles the force relative to full absorption.

Common Mistakes

⚠️
Using 2I/c for an absorbing surface

The factor 2 applies to ideal reversal of photon momentum by reflection. Perfect absorption uses I/c.

⚠️
Confusing intensity with total power

Pressure depends on power per unit area. Divide total beam power by beam area before using I/c.

⚠️
Ignoring incidence angle

At oblique incidence, only the normal momentum component contributes to normal pressure in the simple surface model.

Frequently Asked Questions

Solar sails — viable propulsion?
Force is tiny but constant. Over months/years: significant acceleration. IKAROS (JAXA) demonstrated solar sailing in 2010. Future concepts: laser-driven sails (Breakthrough Starshot) for interstellar travel.
Photon momentum?
p=E/c=hf/c=h/λ. A 1W laser beam carries 3.33×10⁻⁹ N·s of momentum per second. Absorbing surface: all momentum transferred. Reflecting: twice the momentum change (elastic 'bounce').
Why does a massless photon have momentum?
Relativistic energy and momentum are related by E=pc for a massless particle. Therefore a photon of energy E has momentum p=E/c=h/λ even though its rest mass is zero.
Why is pressure doubled for perfect reflection?
An absorbed photon loses its forward momentum to the surface. A perfectly reflected photon reverses direction, so its momentum change is approximately twice as large.
Can radiation pressure move spacecraft?
Yes. Solar sails use the continuous momentum flux from sunlight. The force is small, but in space it can produce useful acceleration over long durations.
Does radiation pressure depend on wavelength at fixed intensity?
For a perfectly absorbing macroscopic surface, p=I/c is independent of wavelength at fixed intensity. Shorter-wavelength photons carry more momentum individually, but there are fewer photons for the same energy flux.
Why does a perfectly reflecting surface feel twice the radiation pressure of an absorber?
An absorbed photon transfers its incoming momentum to the surface. A photon reflected straight back reverses its momentum, producing roughly twice the momentum change. For normal incidence, ideal pressure is I/c for perfect absorption and 2I/c for perfect reflection.

Formula Explorer connections

Interpretation: This relationship connects pressure, velocity, density, viscosity, geometry or transport in a fluid system. Assumption: Check whether flow is steady, incompressible, laminar, fully developed or one-dimensional. Reynolds and Mach regimes determine whether simplified formulas are valid.

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