Choose a light calculation
Photometric outputs describe visible light. Radiometric outputs describe optical power. Use SI units for the clearest comparisons.
Example data table
| Scenario | Known values | Formula | Calculated result |
|---|---|---|---|
| Desk lamp target | 500 cd, 2 m, 0° | Eᵥ = Iᵥ cos(θ) / r² | 125 lux |
| Isotropic optical source | 60 W, 3 m, 100% | Eₑ = P / 4πr² | 0.531 W/m² |
| Laser beam spot | 0.50 W, 10 cm diameter | Eₑ = P / A | 63.662 W/m² |
| Focused lamp beam | 1,600 lm, π sr | Iᵥ = Φᵥ / Ω | 509.296 cd |
Formula used
Illuminance from a point source
Eᵥ = Iᵥ × cos(θ) ÷ r²
Eᵥ is illuminance in lux. Iᵥ is luminous intensity in candela. θ is the incidence angle. r is distance in metres.
Irradiance from an isotropic source
Eₑ = P × T ÷ (4πr²)
Eₑ is irradiance in W/m². P is optical power. T is a transmission fraction. The relationship assumes power spreads uniformly.
Average beam irradiance
Eₑ = P × T ÷ A
A is the illuminated area. This gives an average. Real beams may peak at the centre.
Luminous and radiant intensity
Iᵥ = Φᵥ ÷ Ω
Iₑ = P × T ÷ Ω
Φᵥ is luminous flux in lumens. Ω is solid angle in steradians. These formulas describe directional distributions.
Photon flux
Ṅ = P × T × λ ÷ (hc)
Ṅ is photon flux. λ is wavelength in metres. h is Planck’s constant. c is the speed of light.
How to use this calculator
- Choose the calculation that matches your known measurements.
- Enter source power, luminous intensity, or luminous flux.
- Select units before comparing values from different instruments.
- Enter distance and angle when the target receives directional light.
- Use transmission for filters, lenses, protective covers, or windows.
- Use beam dimensions for lasers, projectors, and focused luminaires.
- Press calculate to display the result above the form.
- Review the table and graph before exporting CSV or PDF.
Understanding light intensity measurements
Light intensity can describe several related quantities. The correct choice depends on the task. A room-lighting check usually needs illuminance. A laser safety review often needs irradiance. An optical design may need radiant intensity or photon flux.
Illuminance uses lux. It measures visible light received by a surface. A lux meter reports this value. The reading changes with distance. It also changes with the surface angle. The cosine factor accounts for that geometry. A tilted surface receives less light.
Candela describes directional visible-light output. It is not the same as lumens. Lumens describe total visible output. Candela describes output within a direction. A narrow beam can have high candela. It may still have modest total lumens.
Radiometric measurements use watts. Irradiance uses watts per square metre. This is useful for ultraviolet, infrared, lasers, and plant lighting research. Electrical input watts are not enough. Use measured optical output when possible. Filters and lenses can reduce delivered power.
The inverse-square rule applies to point-like sources. Double the distance and irradiance becomes one quarter. Real lamps are not perfect points. Large fixtures need more careful geometry. The rule remains a strong first estimate when distance is much larger than fixture size.
Focused beams need a different method. Divide effective optical power by the beam area. Use the footprint at the target plane. Circular beams use πd²/4. Rectangular beams use width times height. This result is an average. Gaussian beams have stronger centres.
Photon flux helps when wavelength matters. Blue, green, and red photons carry different energies. Equal optical power does not mean equal photon count. The photon formula converts power and wavelength into photons per second. This matters in spectroscopy and photochemistry.
Always record units and assumptions. State whether readings are photometric or radiometric. Note distance, angle, beam size, and transmission. Small input errors can create larger output errors. Distance errors are especially important because distance is squared.
Calibration improves confidence. Place the sensor where the calculation defines the target. Keep the sensor face aligned with incoming light. Block stray reflections where possible. Allow lamps to warm up before measuring. Repeat measurements and calculate an average. Record ambient light separately. For pulsed or flickering sources, use equipment with suitable response time. These steps make calculated estimates easier to verify during real field work.
Frequently asked questions
1. What does light intensity mean?
It can mean luminous intensity in candela, radiant intensity in watts per steradian, illuminance in lux, or irradiance in W/m². The correct quantity depends on the measurement goal.
2. What is the difference between lux and candela?
Candela describes directional light output from a source. Lux describes visible light received by a surface. Lux changes with distance and angle. Candela is a source property for a chosen direction.
3. Why does light decrease with distance?
For a point-like source, the same power spreads across a larger spherical area. That area grows with distance squared. Therefore illuminance and irradiance drop according to an inverse-square relationship.
4. When should I use W/m² instead of lux?
Use W/m² when physical optical power matters. It suits ultraviolet, infrared, laser, thermal, scientific, and material applications. Use lux when evaluating visible lighting for people.
5. Does this calculator use electrical power?
No. Enter emitted optical or radiant power. Electrical input power can be much higher. Source efficiency, heat losses, drivers, and optics affect the delivered optical power.
6. What transmission value should I enter?
Enter 100% when no loss applies. Use a lower value for filters, glass, lenses, water, protective covers, or other elements. Multiply individual fractional transmissions when several elements are present.
7. Is the inverse-square rule always exact?
No. It is an ideal point-source model. It works best when measurement distance greatly exceeds source dimensions. Near large fixtures, use measured data, photometric files, or detailed optical modelling.
8. How do I measure beam area?
Measure the illuminated footprint at the target plane. For a circle, measure diameter. For a rectangle, measure width and height. Use a consistent threshold for soft-edged beams.
9. Why does incidence angle affect illuminance?
A tilted surface spreads the same incoming light over more surface area. The cosine law captures this effect. Perpendicular light gives the highest illuminance for the same source and distance.
10. What is a steradian?
A steradian measures solid angle. A full sphere contains 4π steradians. It helps describe how a source distributes flux or power through three-dimensional space.
11. Can I use this result for safety decisions?
Use it as an estimate and planning tool. Safety decisions require calibrated instruments, applicable standards, uncertainty analysis, and professional review. Laser and ultraviolet exposures need particular care.