☀️ Radiation Pressure Calculator
Calculate the pressure exerted by electromagnetic radiation
Sunlight at Earth: ~1,361 W/m² | Laser: 10⁶-10¹² W/m² | Solar surface: ~6.3×10⁷ W/m²
How to Use This Calculator
Enter Radiation Intensity
Input the intensity of the electromagnetic radiation in watts per square meter (W/m²). For sunlight at Earth's distance, this is approximately 1,361 W/m² (the solar constant). For lasers, intensities can be much higher (10⁶ to 10¹² W/m² or more).
Calculate Pressure
Click "Calculate" to determine the radiation pressure. The calculator uses the formula P = I/c for a perfect absorber, where I is intensity and c is the speed of light. The result shows the pressure in pascals (Pa) and force per unit area in newtons per square meter (N/m²).
Understand the Result
Note that radiation pressure is very small for most applications. Sunlight at Earth produces only about 4.5 μPa (micropascals). However, for highly reflective surfaces (like solar sails), the pressure is doubled. In space where there's no atmospheric pressure, even tiny radiation pressure can be significant over time.
Formula
P = I / c
(Perfect absorber)
P = 2I / c
(Perfect reflector)
Where:
- P = Radiation pressure (Pa, pascals)
- I = Radiation intensity (W/m², watts per square meter)
- c = Speed of light = 299,792,458 m/s
- For perfect absorber: P = I/c (photon transfers all momentum)
- For perfect reflector: P = 2I/c (photon bounces back, transferring 2× momentum)
Example Calculation: Sunlight at Earth
Given:
- Solar intensity at Earth: I = 1,361 W/m²
- Speed of light: c = 299,792,458 m/s
- Surface: perfect absorber
Calculation:
P = I / c
P = 1,361 / 299,792,458
P = 4.54 × 10⁻⁶ Pa = 4.54 μPa
This is extremely small - about 10 billion times smaller than atmospheric pressure (101,325 Pa).
Example Calculation: Solar Sail (Perfect Reflector)
Given:
- Solar intensity: I = 1,361 W/m²
- Perfect reflector: pressure is doubled
Calculation:
P = 2I / c
P = 2 × 1,361 / 299,792,458
P = 9.08 × 10⁻⁶ Pa = 9.08 μPa
Even doubled, this is still very small, but in space over long periods, it can accelerate spacecraft.
Key Insights:
- Radiation pressure is proportional to intensity and inversely proportional to speed of light
- For perfect absorber: P = I/c (photon absorbed, transfers momentum p = E/c)
- For perfect reflector: P = 2I/c (photon reflected, transfers 2× momentum)
- Radiation pressure is very small but can be significant in space
- Solar sails use radiation pressure for propulsion without fuel
About the Radiation Pressure Calculator
The Radiation Pressure Calculator determines the pressure exerted by electromagnetic radiation on a surface. This pressure arises from the momentum carried by photons - when light is absorbed or reflected, it transfers momentum to the surface, creating a force. Radiation pressure is fundamental to understanding solar sails, laser propulsion, and the interaction of light with matter.
When to Use This Calculator
- Solar Sail Design: Calculate the force available for spacecraft propulsion
- Laser Applications: Determine pressure from high-intensity lasers
- Optical Physics: Understand photon momentum and light-matter interactions
- Astrophysics: Calculate radiation pressure effects on dust and gas
- Educational Purposes: Learn about electromagnetic momentum and pressure
Why Use Our Calculator?
- ✅ Accurate Formula: Uses the standard radiation pressure equation
- ✅ Multiple Cases: Handles both perfect absorbers and reflectors
- ✅ Educational Tool: Learn about photon momentum and pressure
- ✅ Real Applications: Relevant for solar sails and laser propulsion
- ✅ Free to Use: No registration required
- ✅ Mobile Friendly: Works on all devices
Understanding Radiation Pressure
Radiation pressure comes from the momentum of photons:
- Photon Momentum: p = E/c = hf/c, where E is energy, h is Planck's constant, f is frequency
- Absorption: When a photon is absorbed, it transfers all its momentum to the surface
- Reflection: When a photon is reflected, it reverses direction, transferring twice the momentum
- Intensity: I = power per unit area = energy flux (W/m²)
- Pressure: P = momentum flux = (I/c) for absorption, (2I/c) for reflection
Derivation
For a perfect absorber:
- Each photon carries momentum: p = E/c
- Intensity I = energy per unit area per unit time
- Number of photons per unit area per unit time = I / (energy per photon)
- Momentum per unit area per unit time = (I / E) × (E/c) = I/c
- This momentum transfer rate equals pressure: P = I/c
For a perfect reflector, momentum change is doubled (photon reverses direction):
P = 2I/c
Real-World Applications
- Solar Sails: Large reflective sails use radiation pressure for spacecraft propulsion without fuel
- Laser Propulsion: High-intensity lasers can push objects using radiation pressure
- Optical Tweezers: Use radiation pressure to trap and manipulate microscopic particles
- Stellar Physics: Radiation pressure counteracts gravity in massive stars
- Comet Tails: Solar radiation pressure pushes dust particles away from comets
- Dust Dynamics: Radiation pressure affects the motion of dust grains in space
Tips for Using This Calculator
- Radiation pressure is very small - sunlight at Earth produces only ~4.5 μPa
- For perfect reflectors, multiply the result by 2
- Real surfaces have reflectivity between 0 and 1 - actual pressure lies between I/c and 2I/c
- In space (no atmosphere), even tiny radiation pressure can be significant over time
- Solar sails need large surface areas to generate meaningful acceleration
Frequently Asked Questions
What is radiation pressure?
Radiation pressure is the pressure exerted by electromagnetic radiation (light) on a surface. It arises because photons carry momentum, and when they're absorbed or reflected, they transfer this momentum to the surface, creating a force. The pressure is proportional to the radiation intensity and inversely proportional to the speed of light.
Why is radiation pressure doubled for a perfect reflector?
When a photon is reflected, it reverses direction. The momentum change is Δp = p_final - p_initial = (-p) - p = -2p, where p is the photon's momentum. The surface experiences a force equal to this momentum change, so the pressure is P = 2I/c, twice that of a perfect absorber where P = I/c.
How strong is radiation pressure from sunlight?
At Earth's distance from the Sun, solar radiation intensity is about 1,361 W/m². This produces a radiation pressure of approximately 4.54 × 10⁻⁶ Pa (4.54 micropascals) for a perfect absorber, or about 9.08 μPa for a perfect reflector. This is extremely small - about 10 billion times smaller than atmospheric pressure at sea level (101,325 Pa).
Can radiation pressure be used for propulsion?
Yes! Solar sails use radiation pressure for spacecraft propulsion. By deploying large, lightweight reflective sails, spacecraft can accelerate continuously using sunlight, without needing fuel. The force is small but constant, and over time can reach significant speeds. Several missions have successfully demonstrated solar sail technology, including Japan's IKAROS and NASA's LightSail missions.
Does radiation pressure affect stars?
Yes, radiation pressure is important in stellar physics. In massive stars, the intense radiation from nuclear fusion creates outward radiation pressure that counteracts gravity. This is one of the forces that maintains stellar equilibrium. For very massive stars, radiation pressure can become so strong that it causes stellar winds and mass loss.
How does radiation pressure compare to other forces?
Radiation pressure is typically much weaker than gravitational, electromagnetic, or nuclear forces. However, it's significant in specific contexts: in space where there's no atmosphere, for large reflective surfaces (solar sails), for high-intensity lasers, and in stellar interiors. The key advantage is that radiation pressure requires no fuel and can operate continuously.