Luminous Intensity Calculator

Work out luminous intensity instantly with clear inputs, formula shown and shareable results.

About Luminous Intensity Calculator

Luminous intensity is flux per unit solid angle, measured in candela. A 60 degree beam subtends 0.842 steradians, so 1200 lumens concentrated into it gives about 1425 cd. Narrowing the beam raises intensity without changing the lamp's output, which is why spotlights read so high in candela.

Formulas

Luminous intensity

I = flux / solid angle

Cone solid angle

omega = 2 pi (1 - cos(half angle))

Worked example

With the default values below, Luminous Intensity Calculator returns Luminous Intensity of 1,425.54. Change any input above and every figure here is recalculated in your browser.

Inputs used

Luminous fluxminimum 0 lm: 1,200 lm
Beam angleaccepts 0–360 deg: 60 deg

Results

Luminous Intensity: 1,425.54 cd
Beam Solid Angle: 0.8418 sr
Illuminance At 2 Metres: 356.385 lx
Half Angle: 30.00 deg

Step by step

1Values used
2Luminous intensity
3Cone solid angle
4Luminous Intensity= 1,425.54 cd
5Beam Solid Angle= 0.8418 sr
6Illuminance At 2 Metres= 356.385 lx
7Half Angle= 30.00 deg

Assumptions and limits

The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Why does a narrow beam have such high candela?

Because the same flux is squeezed into a smaller solid angle. A torch rated at thousands of candela may emit only a few hundred lumens.

What is the solid angle of a full sphere?

4 pi, about 12.57 steradians. An omnidirectional lamp divides its lumens by that figure.