Radiation Pressure Calculator
Enter the light intensity I, area A, and reflectivity r to compute the electromagnetic radiation pressure P=(1+r)I/c and the radiation force F=P·A. Fully absorbing: P=I/c; fully reflecting: P=2I/c.
Input Data
Results
At a glance:Radiation pressure: electromagnetic waves (light) carry momentum; when they strike a surface they transfer that momentum to it, producing a small pressure. Let the intensity be I (W/m²), the speed of light c (299792458 m/s), and the surface reflectivity r (0=fully absorbing, 1=fully reflecting). For full absorption each photon is absorbed and its entire momentum is transferred, giving P=I/c. For full reflection the photon bounces back, doubling the momentum change, giving P=2I/c. For a general surface: P=(1+r)·I/c. The radiation force is F=P·A (A is the illuminated area). At Earth's orbit the solar constant is I=1361 W/m²: full absorption gives P=1361/3e8≈4.54e-6 Pa=4.54 μPa and a 1 m² surface feels 4.54 μN; full reflection gives P≈9.08 μPa and 9.08 μN — less than the weight of a mosquito, yet the effect accumulates over large areas and long times. Applications: (1) solar-sail spacecraft use large reflecting sails (e.g. IKAROS 200 m², LightSail 32 m²) to build up velocity from light pressure in the drag-free vacuum of space, theoretically reaching ~10% of light speed; (2) comet tails pointing away from the Sun are driven mainly by radiation pressure on dust (solar wind is the other cause); (3) laser cooling and optical tweezers use light pressure to manipulate atoms and cells; (4) measuring radiation pressure was a key test of electromagnetic theory (first measured by Lebedev in 1900). History: Maxwell's 1873 electromagnetic theory predicted radiation pressure; Lebedev confirmed it experimentally in 1900; mass–energy equivalence E=mc² and photon momentum p=E/c provide the microscopic explanation.
Formula
Fully absorbing: P = I / c
Fully reflecting: P = 2I / c
General case: P = (1 + r) · I / c
Radiation force: F = P · A
Photon momentum: p = E / c = h·f / c = h / λ
$$P = \frac{(1+r)I}{c}$$$$F = PA, \quad p_{\text{photon}} = \frac{E}{c}$$How to Use
- Enter the light intensity I (W/m²), illuminated area A (m²), and reflectivity r (0–1).
- The calculator returns the radiation pressure P=(1+r)I/c and the radiation force F=P·A.
- r=0 is fully absorbing and r=1 is fully reflecting; values outside range are clamped to [0,1].
Case Studies
Solar sail thrust
A 100 m × 100 m sail (A=1e4 m²) at Earth's orbit with r≈1 feels F≈2·9.08e-6·1e4≈0.18 N from sunlight alone.
With no atmospheric drag, continuous light pressure slowly but steadily accelerates the craft.
Missions such as IKAROS and LightSail demonstrate the principle in practice.
Comet dust tails
Radiation pressure pushes micrometre-scale dust away from the Sun, forming the curved dust tail.
The effect is distinguishable from the ion tail driven by the solar wind.
This is a direct, visible consequence of light carrying momentum.
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.