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Lumen to Candela Calculator

Convert lumens (lm) to candela (cd) using beam angle: cd = lm ÷ 2π(1 − cos(θ/2)). Reverse candela to lumens. 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 intensity from flux and full beam angle, or flux from intensity 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
  • I = Φ / Ω; Ω = 2π(1 − cos(θ/2)) for a cone
Specification basis

Formulas

Core equations used by this calculator.

Candela from lumenscd = lm ÷ 2π(1 − cos(θ/2))
Solid angleΩ = 2π(1 − cos(θ/2))
Lumens from candelalm = cd × Ω
Full spherecd ≈ lm ÷ 4π ≈ lm ÷ 12.566
iθ is the full beam (apex) angle in degrees. Assumes uniform intensity over the cone. Real LEDs and fixtures are non-uniform — use photometry for design-critical work. Narrow beams (e.g. ≤90°) match this model better than very wide flood patterns.

How to use

1

Choose direction

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

2

Enter lumens (or candela) and full beam angle

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

3

Read candela or lumens

Result assumes uniform intensity over the cone solid angle.

Example calculations

Common configurations with formula and result.

ϟ

1000 lm · 60°

Default

1000 ÷ 2π(1 − cos(30°))
≈ 1187.95 cd
ϟ

12.566 lm · full sphere

θ = 360° → Ω = 4π

12.566 ÷ 4π
≈ 1 cd
ϟ

100 lm · 1 sr

Φ ÷ Ω

100 ÷ 1
100 cd
ϟ

Narrow spotlight

1000 lm · 10°

1000 ÷ 2π(1 − cos(5°))
≈ 41,825 cd
ϟ

cd → lm

500 cd · 60°

500 × Ω(60°)
≈ 420.86 lm

Solid angle Ω vs full beam angle θ

Common values at a glance.

θ (full)Ω (sr)cd per lm
10°0.023941.82
30°0.2144.67
60°0.8421.188
90°1.8400.543
120°3.1420.318
180°6.2830.159
360°12.5660.080
i cd = lm ÷ Ω. Narrower beams → smaller Ω → higher candela for the same lumens (light is more concentrated).

Lumen to Candela 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
Lumens (lm) measure total luminous flux; candela (cd) measures luminous intensity in a direction. For a uniform cone beam with full apex angle θ, I = Φ / Ω with Ω = 2π(1 − cos(θ/2)). So cd = lm ÷ 2π(1 − cos(θ/2)). A full sphere is Ω = 4π sr, so ≈12.57 lm isotropic ≈ 1 cd.
What it calculates
Luminous intensity from flux and full beam angle, or flux from intensity and angle.
Inputs
  • Lumens (lm) or candela (cd)
  • Full beam angle θ in degrees
Outputs
  • Candela (lm → cd) or lumens (cd → lm)
Formula
Ω=2π(1−cos(θ/2)); I=Φ/Ω
Assumptions
  • Uniform intensity over a circular cone
  • θ is full apex angle
Units
  • lm, ° → cd
Boundary conditions
  • θ = 0 → Ω = 0 → undefined intensity (UI returns 0)
  • θ = 360° → Ω = 4π
Example
1000 lm, 60° → ≈ 1187.95 cd
Validation cases

3 published on this page

  • 1000 lm, 60° → ≈ 1187.95 cd
  • 12.566 lm, 360° → ≈ 1 cd
  • 500 cd, 60° → lm → ≈ 420.86 lm
Specification basis
  • I = Φ / Ω; Ω = 2π(1 − cos(θ/2)) for a cone
Calculation version
1.1.0

Background

Interpretation and common distinctions.

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

I((cd)) = (Phi((lm)))/(2π(1 − cosfracθ2))

Default: 1000 lm · 60° → ≈ 1187.95 cd.

Lumens vs candela vs lux

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

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

Solid angle

Ω((sr)) = 2π(1 − cos(θ)/2)

Then I = Phi / Ω.

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

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

lm Candela to Lumen › mcd Lumen to mcd › lx Candela to Lux › lx Lumen to Lux ›
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Frequently asked questions

Key distinctions behind the calculation.

How do I convert lumens to candela?

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

What is the difference between lumens and candela?

Lumens are total visible light output. Candela is directional intensity (how bright in one direction). A narrow beam can have high candela with modest total lumens.

What is the solid angle Ω?

Ω = 2π(1 − cos(θ/2)) steradians for a circular cone with full apex angle θ. Then cd = lm ÷ Ω.

Is θ the half-angle or full angle?

This calculator uses the full apex / beam angle. If a datasheet lists ±30°, enter 60°. Some LED sheets quote the 50% intensity (FWHM) angle — use that full width.

Does 12.57 lm equal 1 cd?

Only for an isotropic source over a full sphere (Ω = 4π). Directional lamps use a smaller Ω, so candela is much higher than lm / 12.57.

Why do some tools show millicandela (mcd)?

Indicator LEDs are often rated in mcd (1 cd = 1000 mcd). Convert with lumen to mcd, or multiply this result by 1000.

Is the formula accurate for wide beams (e.g. 120°)?

It is exact for a perfectly uniform cone. Real wide-angle LEDs are non-uniform, so treat results as estimates; photometry is better for design.

Can I convert candela back to lumens?

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