Radiant Intensity Calculator

1. Select a calculation method that matches your data.
2. Choose the quantity you want to solve for.
3. Enter the known values and select their units.
4. Click Calculate to show the result above the form.
5. Use Download CSV or Download PDF for reporting.

1) What Radiant Intensity Represents

Radiant intensity (I) describes how much radiant power is sent in a particular direction per unit solid angle. It is measured in watts per steradian (W/sr). Unlike total radiant flux, which sums all emitted power, radiant intensity focuses on directionality, which matters for beams, reflectors, and collimated sources.

2) Typical Magnitudes and Practical Ranges

Values vary widely. A small indicator LED might deliver micro-watts into a broad pattern, producing low W/sr. A well-collimated laser can concentrate watts into a tiny solid angle, producing very high W/sr. This calculator supports milli-, base-, and kilo- scaling so you can keep inputs readable.

3) Solid Angle Data You Can Use

Full space is 4π sr (about 12.566 sr). A hemisphere is 2π sr (about 6.283 sr). A narrow cone can be estimated with Ω ≈ 2π(1 − cos(θ/2)), where θ is the full cone angle. If your instrument reports square degrees, the tool converts deg^2 to steradians automatically.

4) Flux Method for Measured Power

When you know radiant flux Φ within a known beam spread, use I = Φ/Ω. For example, Φ = 10 W distributed into Ω = 0.5 sr gives I = 20 W/sr. This is common in optical benches, integrating-sphere measurements paired with angular characterization, and in simplified lighting models.

5) Energy-Time Method for Pulses

For pulsed sources, energy Q is often measured per pulse or over a window. Convert energy to average power using Φ = Q/t, then apply I = Φ/Ω, or directly I = Q/(t·Ω). Example: Q = 50 J over t = 2 s into Ω = 0.25 sr produces I = 100 W/sr.

6) Data Quality and Uncertainty

Uncertainty typically comes from Ω. A small angular error can change Ω significantly for tight beams, which directly scales I. Record how Ω was obtained (goniometer, beam profiler, or a cone-angle estimate). If you need traceability, keep SI values and export the result table.

7) Unit Handling and Reporting

The calculator normalizes inputs internally to SI, then shows both selected-unit and SI outputs. This reduces mistakes when mixing mW, W, and kW, or when converting deg^2 to sr. CSV exports are useful for spreadsheets, while the PDF keeps a clean calculation snapshot for reports.

8) Common Use Cases in Engineering

Radiant intensity supports optical simulation, safety analysis, sensor saturation checks, and thermal loading estimates. It is also a helpful bridge to radiance and irradiance models when geometry is known. Use this tool to compare different optics, alignments, or beam spreads using consistent assumptions.

1) Is radiant intensity the same as candela?

No. Candela is luminous intensity, weighted by human vision. Radiant intensity is purely physical power per steradian across all wavelengths.

2) What solid angle should I use for a full sphere?

Use 4π sr, which is about 12.566 sr. For a hemisphere, use 2π sr, about 6.283 sr.

3) How do I estimate a cone solid angle from beam angle?

For a cone with full angle θ, use Ω ≈ 2π(1 − cos(θ/2)). Ensure θ is in radians when using cosine.

4) Why does a smaller solid angle increase intensity?

Because I = Φ/Ω. If the same power is focused into fewer steradians, power per steradian rises proportionally.

5) Can I use square degrees instead of steradians?

Yes. Select deg^2 for Ω units, and the calculator converts to steradians internally for computation and SI reporting.

6) Which method should I choose: flux or energy?

Use flux if you measured power directly. Use energy if you measured joules over a time window or pulse train and know the duration.

7) What if my beam is not uniform within the angle?

This calculator assumes average distribution within the stated Ω. For non-uniform beams, use a measured angular distribution or report intensity for a defined acceptance angle.