Lumens ⇄ Candela Converter (beam angle)

Understanding the lumens to candela converter — concept and principle

Lamp boxes give luminous flux in lumens (lm), the total visible light a source emits, while spotlights, flashlights and LED datasheets often quote luminous intensity in candela (cd), how bright the light is in one direction. Converting between them needs the beam angle. Use this converter to compare a 36° spotlight with a bare bulb, estimate the centre intensity of a flashlight or work out the lumens behind a candela rating.

How it is calculated

The calculator assumes the light fills a cone evenly. A cone with full apex angle θ covers a solid angle

Ω = 2π × (1 − cos(θ ÷ 2)) steradians (sr).

• Lumens → candela: I (cd) = Φ (lm) ÷ Ω
• Candela → lumens: Φ (lm) = I (cd) × Ω

A beam angle of 360° gives the full sphere, Ω = 4π ≈ 12.566 sr; 180° gives a hemisphere, 2π sr. The angle must be between 1° and 360°.

The principle

The candela is the SI base unit of luminous intensity, and the lumen is defined from it: 1 lm = 1 cd × 1 sr. A steradian is the solid angle that cuts an area of r² from a sphere of radius r, and a whole sphere has 4π sr. If a source sends the same intensity into every part of a cone, its flux is simply intensity times the cone's solid angle. The cone formula comes from integrating over the spherical cap that the cone cuts from a unit sphere. Squeezing the same lumens into a narrower cone shrinks Ω, so the candela rises sharply: 800 lm in a 36° beam is about 2,600 cd.

Worked example

1. Default inputs: lumens → candela, value 800 lm, beam angle 360°.
2. Solid angle: Ω = 2π × (1 − cos 180°) = 2π × 2 = 4π = 12.56637061 sr.
3. Intensity: 800 ÷ 12.56637061 = 63.66197724 cd.

How to read the result

The result is an average intensity across the beam. Real lamps are brighter at the centre and fade towards the edge, and many datasheets define the beam angle as the angle where intensity drops to half its peak, with some light falling outside it. The true peak candela of a spotlight is therefore usually higher than this estimate, and the lumens inside the stated beam are lower than the lamp's total. Use candela to compare how far a beam throws: illuminance on a surface facing the lamp is E (lux) = I (cd) ÷ d² (m), so 2,600 cd gives about 650 lx at 2 m.

Common mistakes

• Using the half angle instead of the full beam angle; the formula already halves it.
• Treating a bare omnidirectional bulb as a 360° beam when its base blocks part of the light.
• Confusing candela with lux; lux depends on distance, candela does not.

Frequently asked questions

How many candela is an 800-lumen bulb?

About 63.7 cd if it shone evenly in every direction.

How many lumens is 1 candela?

A uniform 1 cd source in all directions emits 4π ≈ 12.57 lm.

Why does a narrow beam have more candela?

The same lumens go into a smaller solid angle, so more light is sent in each direction.

What is the solid angle of a 60° beam?

2π × (1 − cos 30°) ≈ 0.842 sr.

Sources: BIPM, The International System of Units (SI Brochure), 9th edition, 2019 (candela, lumen) · CIE S 017, ILV: International Lighting Vocabulary