Lighting calculator

Candela to Lumen Calculator

Convert candela (cd) to lumens (lm) using beam angle: lm = cd × 2π(1 − cos(θ/2)). Reverse lumens to candela. Includes solid angle and full-sphere 4π.

Instant result

Result

—

Enter values to calculate.

Inputs—

Mode—

Formula—

Trust summary Engine tested · Specification checked · v1.1.0

Input interpretation: Enter values to calculate.
Result: —
Model: Luminous flux from intensity and full beam angle, or intensity from flux and angle.
Scope: Uniform intensity over a circular cone
Verification: Engine tested · Specification checked · v1.1.0
Named expert review: Optional · Not performed
Specification basis: Φ = I × Ω; Ω = 2π(1 − cos(θ/2)) for a cone
Specification basis

Formulas

Core equations used by this calculator.

Lumens from candelalm = cd × 2π(1 − cos(θ/2))

Solid angleΩ = 2π(1 − cos(θ/2))

Candela from lumenscd = lm ÷ Ω

Full spherelm ≈ cd × 4π ≈ cd × 12.566

iθ is the full beam (apex) angle in degrees. Assumes uniform intensity over the cone. Real fixtures have non-uniform beams — use photometry for design-critical work. Candlepower is an older name for candela.

How to use

Choose direction

cd → lm for flux from intensity, or lm → cd for the reverse.

Enter candela (or lumens) and full beam angle

Use the manufacturer’s full beam angle in degrees (e.g. 60°, not ±30°).

Read lumens or candela

Result assumes uniform intensity over the cone solid angle.

Example calculations

Common configurations with formula and result.

500 cd · 60°

Default check

500 × 2π(1 − cos(30°))

≈ 420.86 lm

1 cd · full sphere

θ = 360° → Ω = 4π

1 × 4π

≈ 12.566 lm

100 cd · 1 sr equivalent

Intensity × solid angle

100 × 1

100 lm

Narrow spotlight

1000 cd · 10°

1000 × 2π(1 − cos(5°))

≈ 23.91 lm

lm → cd

1000 lm · 60°

1000 ÷ Ω(60°)

≈ 1188.0 cd

Solid angle Ω vs full beam angle θ

Common values at a glance.

θ (full)	Ω (sr)	lm per cd
10°	0.0239	0.0239
30°	0.214	0.214
60°	0.842	0.842
90°	1.840	1.840
120°	3.142	π
180°	6.283	2π
360°	12.566	4π

i lm = cd × Ω. Narrower beams → smaller Ω → fewer total lumens for the same candela (light is more concentrated).

Candela to Lumen calculator specification

Version 1.1.0 · Engine tested

Calculation status

Engine tested 3 published cases
Named expert review Not performed
Calculation version 1.1.0

Review policy

Definition: Candela (cd) measures luminous intensity in a direction; lumens (lm) measure total luminous flux. For a uniform cone beam with full apex angle θ, Φ = I × Ω with Ω = 2π(1 − cos(θ/2)). So lm = cd × 2π(1 − cos(θ/2)). A full sphere is Ω = 4π sr, so 1 cd isotropic ≈ 12.57 lm.
What it calculates: Luminous flux from intensity and full beam angle, or intensity from flux and angle.
Inputs: Candela (cd) or lumens (lm)
Full beam angle θ in degrees
Outputs: Lumens (cd → lm) or candela (lm → cd)
Formula: Ω=2π(1−cos(θ/2)); Φ=I·Ω
Assumptions: Uniform intensity over a circular cone
θ is full apex angle
Units: cd, ° → lm
Boundary conditions: θ = 0 → Ω = 0 → flux 0
θ = 360° → Ω = 4π
Example: 500 cd, 60° → ≈ 420.86 lm
Validation cases: 3 published on this page
500 cd, 60° → ≈ 420.86 lm
1 cd, 360° → ≈ 12.566 lm
1000 lm, 60° → cd → ≈ 1188.0 cd
Specification basis: Φ = I × Ω; Ω = 2π(1 − cos(θ/2)) for a cone
Calculation version: 1.1.0

Background

Interpretation and common distinctions.

Convert candela (cd) to lumens (lm) using the full beam (apex) angle.

Phi((lm)) = I((cd)) × 2π(1 − cos(θ)/2)

Default: 500 cd · 60° → ≈ 420.86 lm.

Candela vs lumens vs lux

Unit	Measures
Candela (cd)	Luminous intensity in a direction
Lumen (lm)	Total luminous flux (all light output)
Lux (lx)	Illuminance on a surface (lm/m²)

You need a beam angle (or solid angle) to relate cd and lm. Comparing products: use the same unit — don’t treat cd and lm as interchangeable.

Solid angle

Ω((sr)) = 2π(1 − cos(θ)/2)

Then Phi = I × Ω.

Full sphere: θ = 360° → Ω = 4π ≈ 12.566 sr → 1 cd ≈ 12.57 lm (isotropic)
Hemisphere: θ = 180° → Ω = 2π

Other calculators in this family: Lumen to Candela, Candela to Lux, Lumen to Lux, Lumen to mcd .

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Frequently asked questions

Key distinctions behind the calculation.

How do I convert candela to lumens?

Multiply by the beam solid angle: lm = cd × 2π(1 − cos(θ/2)), where θ is the full beam angle in degrees. You cannot convert cd to lm without a beam angle (or solid angle).

What is the difference between candela and lumens?

Candela is directional intensity (how bright in one direction). Lumens are total visible light output. A narrow high-cd beam can look brighter on a target while emitting fewer total lumens than a wide flood.

Is 1 candela equal to 12.57 lumens?

Only for an isotropic source radiating over a full sphere (Ω = 4π sr). Directional lamps use a much smaller Ω, so lm ≪ 12.57 × cd.

Is θ the half-angle or full angle?

This calculator uses the full apex / beam angle. If a datasheet lists ±30°, enter 60°.

What about lux?

Lux is illuminance on a surface (lm/m²). Candela relates to lux at distance for a point source (roughly E = I / d²). Use candela to lux for that path.

Does beam uniformity matter?

Yes. The formula assumes constant intensity inside the cone. Real LEDs and reflectors vary — photometric files (IES) are better for precise design.

Can I convert lumens back to candela?

Yes — use lm → cd: cd = lm ÷ Ω with the same beam angle.