Lumens to Candela Calculator
Convert luminous flux in lumens (lm) to luminous intensity in candela (cd) for a beam with a given cone apex angle. Enter the lumens and the apex angle in degrees, and press Calculate to get candela. Everything runs locally in your browser.
Enter the luminous flux
Type the total luminous flux of the source in lumens (lm) — the value usually printed on lamp and LED packaging. Zero is valid (0 lm gives 0 cd); negative values are rejected.
Enter the apex angle
Type the full cone apex angle θ in degrees that the beam spreads into. It must be greater than 0° and at most 360° (a full sphere). A narrow spotlight has a small angle; an omnidirectional bulb is 360°.
Press Calculate, read candela
The luminous intensity appears in candela, shown with up to six decimals, together with the solid angle Ω = 2π(1 − cos(θ/2)) in steradians. Press Reset to clear everything and start over.
Lumens to candela calculation
- How do you convert lumens to candela?
- For a uniform, isotropic light source inside a cone, the luminous intensity Iv in candela (cd) equals the luminous flux Φv in lumens (lm) divided by the solid angle Ω in steradians (sr): Iv(cd) = Φv(lm) / Ω(sr). The solid angle of a cone with apex angle θ is Ω(sr) = 2π(1 − cos(θ/2)), so cd = lm / (2π(1 − cos(º/2))). For example, 700 lm in a 120° cone gives 700 / π ≈ 222.817 cd.
- What apex angle should I use?
- The apex (beam) angle is the full opening angle of the cone the light spreads into, measured vertex-to-edge across the beam — not the half angle. Typical spotlights are around 10–40°, floodlights around 60–120°, and an omnidirectional bare bulb radiates into a full 360° sphere. This calculator accepts angles greater than 0° and up to 360°.
- What does a 360° apex angle mean?
- A 360° cone is a full sphere, whose solid angle is 4π steradians — the isotropic case: Iv = Φv / 4π. A 1000 lm omnidirectional bulb therefore emits about 79.577 cd on average in every direction. A 180° hemisphere gives Ω = 2π sr instead.
- Why does the same lamp get more candela when the beam is narrower?
- Lumens count all the light; candela counts how densely that light is concentrated in one direction. Halving the cone squeezes the same flux into a smaller solid angle, so intensity rises: 100 lm spread over a 10° cone is about 4182.452 cd, while the same 100 lm over 120° is only about 31.8 cd.
- When is this conversion not accurate?
- The formula assumes the flux is spread uniformly across the cone (a uniform source over the solid angle). Real reflectors and lenses produce peaked hotspots and spill, so real candela varies with direction — treat this as the average intensity over the cone and use a lux meter at distance d (cd ≈ lux × d²) for the true peak.
- How do I go back from candela to lumens?
- Use the inverse relation Φv = Iv × 2π(1 − cos(θ/2)) with our candela to lumens calculator.
Related: Candela to lumens calculator.
Privacy: every calculation runs in your browser tab — no value you type is sent anywhere. Results are averages over the ideal cone and assume a uniform source; verify real fixtures with a lux meter.