Candela to Lumens Converter Formula

Understand the math behind the candela to lumens converter. Each variable explained with a worked example.

Use the Candela to Lumens Converter

Formulas Used

Lumens

lumens = candela * 2 * pi * (1 - cos(beam_angle / 2 * pi / 180))

Variables

VariableDescriptionDefault
candelaCandela (cd)(cd)100
beam_angleBeam Angle(degrees)120

How It Works

Candela to Lumens

Lumens = Candela x 2pi x (1 - cos(theta/2))

Where theta is the beam angle in radians.

  • Candela measures intensity in a specific direction
  • Lumens measure total light output in all directions of the beam

    • A narrow-beam spotlight and a wide floodlight can have the same candela but very different lumens.

    Worked Example

    100 candela light source with 120° beam angle.

    candela = 100beam_angle = 120
    1. 01theta/2 = 60° = pi/3 radians
    2. 02cos(60°) = 0.5
    3. 03Lumens = 100 x 2pi x (1 - 0.5) = 314.2 lumens

    Ready to run the numbers?

    Open Candela to Lumens Converter