Candela and lumens aren’t a fixed conversion — they’re linked by how wide the beam is. Give the intensity (candela) and the beam angle, and this finds the total light output (lumens).
Φ = lumens I = candela Ω = solid angle (steradians)
Why the beam angle is essential
There’s no universal “1 cd = X lm.” The same intensity spread over a wider cone delivers more total lumens; squeezed into a narrow cone it delivers fewer — but each of those lumens hits harder. Anyone quoting a fixed candela–lumen number is skipping the part that matters.
| Beam angle | Solid angle Ω | Total lumens |
|---|---|---|
| 10° | 0.024 sr | 24 lm |
| 24° | 0.137 sr | 137 lm |
| 40° | 0.379 sr | 379 lm |
| 60° | 0.842 sr | 842 lm |
| 90° | 1.840 sr | 1,840 lm |
Why two fixtures with the same lumens look different
1000 lm spotlight vs 1000 lm floodlight
Same total lumens, but the spotlight packs them into a tight beam, so its centre-beam candlepower (CBCP) — the candela straight down the middle — is far higher. It looks dramatically brighter where it’s aimed. The floodlight spreads the same lumens thin, so its CBCP is low and the light feels soft and even.
That’s the whole trick: lumens measure how much light; candela measures how concentrated it is.
CBCP — center beam candlepower
CBCP is just the candela value at the centre of the beam (θ = 0°), the number manufacturers print for spotlights and track heads. It’s what you compare when choosing how “punchy” an accent light will be.
Related calculators
Worked example: 1000 cd over a 30° beam → Ω = 2π(1 − cos 15°) = 0.214 sr, so Φ = 1000 × 0.214 = 214 lm. Assumes an even beam; real optics taper, so treat it as a close estimate.