Radiant Power Calculator

Core relationships

• Φ = E × A where E is irradiance (W/m²) and A is area (m²).
• Φ = I × Ω where I is radiant intensity (W/sr) and Ω is solid angle (sr).
• Φ = M × A where M is radiant exitance (W/m²) and A is emitting area (m²).
• Φ = E_r / t where E_r is radiant energy (J) and t is time (s).

Notes on units

The calculator converts inputs into SI units internally, then returns the solved quantity. Use consistent geometry for area and solid angle to avoid systematic errors.

1. Select a calculation method that matches your measurements.
2. Choose what you want to solve for in the next menu.
3. Enter the remaining quantities and select their units.
4. Press Calculate to view the result above the form.
5. Use Download CSV or Download PDF to export.

1) What radiant power represents

Radiant power (Φ) is the total optical energy emitted, transferred, or received per second. It is measured in watts, and it is a starting point for comparing sources such as LEDs, lamps, and lasers, regardless of beam shape.

2) Connecting power to irradiance

When you know the illuminated area, irradiance (E) links directly to power through Φ = E × A. This supports detector work, solar testing, and exposure checks where the footprint is measurable and the average level is meaningful.

3) Directional emission and solid angle

For directional emitters, radiant intensity (I) describes power per unit solid angle (W/sr). The relationship Φ = I × Ω estimates total output if the emission cone is known. Narrow beams require careful geometry because small Ω errors can shift results.

4) Emitting surfaces and exitance

Radiant exitance (M) is emitted power per unit area from a surface. Using Φ = M × A is common in thermal radiation and hot-surface assessments. It helps when the source is a panel, filament, or heated plate with a defined emitting region.

5) Pulses and energy over time

For pulsed systems, average radiant power follows Φ = E_r / t. Energy in joules may come from a pulse-energy meter, while time can be pulse duration or a measurement window. This mode also supports integrating sensors that report total energy.

6) Unit handling and conversions

This calculator converts inputs to SI internally, then performs the selected solve step. Conversions like mW/cm² to W/m² or msr to sr reduce manual mistakes. Always confirm that the area and angular definitions match your setup.

7) Data quality and uncertainty

Radiant-power estimates are only as good as the measurements behind them. Nonuniform beams, misaligned apertures, and partial collection can bias results. When possible, repeat measurements, record geometry, and note instrument calibration and wavelength limits.

8) Typical workflows

A practical workflow is to measure a footprint, compute power from irradiance, and compare against a rating. For sources with known optics, compute power from intensity and solid angle. For pulsed sources, use energy and time to validate average output.

1) What is the difference between radiant power and radiant intensity?

Radiant power is total optical output in watts. Radiant intensity is power per solid angle in W/sr, describing how concentrated the emission is in a direction.

2) When should I use the irradiance × area method?

Use it when you know the average irradiance over a defined area, such as a beam footprint on a target. It works best when the field is close to uniform.

3) How do I estimate the solid angle for a cone?

For a circular cone with half-angle θ, solid angle is Ω = 2π(1 − cosθ). Ensure θ matches the emission or collection geometry used in your setup.

4) Can I compute power from exitance for a hot surface?

Yes. If you know radiant exitance M (W/m²) and emitting area A, then Φ = M × A. This is useful for plates, panels, and other extended emitters.

5) What does the energy ÷ time mode represent?

It gives average radiant power over the chosen time interval. For pulses, energy may be per pulse, and time may be pulse duration or a measurement window.

6) Why do my results change when I switch units?

If the physical inputs are identical, results should match. Differences usually indicate an incorrect unit choice, a scale mismatch, or inconsistent area and footprint values.

7) Is this calculator suitable for safety exposure calculations?

It can support early estimates, but safety decisions need standards-based limits, spectral weighting, and verified procedures. Use calibrated instruments and consult relevant guidelines for final evaluations.