Lumen Calculator (Lumen to Lux to Candela)

Enter a light source's luminous flux (lumens) and beam angle to find its luminous intensity (candela, I = Φ / Ω) and illuminance at a chosen distance (lux, E = I / d²), using the standard solid-angle and inverse-square-law formulas.

Quick Facts

Illuminance (inverse-square law)
E = I / d²
Illuminance falls off with the square of the distance from a point-like source.
Luminous intensity
I = Φ / Ω
Total lumens divided by the solid angle the beam covers, in steradians.
Solid angle of a cone
Ω = 2π(1 − cos(θ/2))
θ is the full beam angle in degrees; a full sphere equals 4π ≈ 12.57 sr.
Lux and footcandles
1 fc ≈ 10.764 lx
A footcandle is 1 lumen per square foot; a lux is 1 lumen per square meter.

Your Results

Calculated
Illuminance
-
E = I / d², in lux (lm/m²)
Luminous Intensity
-
I = Φ / Ω, in candela
Illuminance
-
Same value in footcandles (lm/ft²)
Beam Solid Angle
-
Ω = 2π(1 − cos(θ/2)), in steradians

Ready

Enter luminous flux, beam angle, and distance, then press Calculate.

Formula and Method for the Lumen to Lux to Candela Calculator

Lumens, candela, and lux describe light from three different angles. Lumens (lm) measure total luminous flux — the total quantity of visible light a source emits in every direction. Candela (cd) measures luminous intensity — the flux concentrated into a specific direction. Lux (lx) measures illuminance — the flux that actually lands on a surface per unit area. This calculator converts a source's total lumens into candela and lux by combining the beam's solid angle with the inverse-square law, so you can estimate how bright a light will appear at a given working distance.

How the calculation works

Enter the source's total luminous flux in lumens and its beam angle — the full apex angle of the cone of light, in degrees (most spotlights, flashlights, and LED bulbs list this figure on the packaging or spec sheet). The calculator first converts the beam angle into a solid angle using Ω = 2π(1 − cos(θ/2)) steradians, then divides the lumens by that solid angle to get luminous intensity: I = Φ / Ω (candela). Finally, it applies the inverse-square law, E = I / d², to find illuminance in lux at the distance you specify. Light spreads out over an ever-larger area as it travels away from the source, so illuminance drops with the square of the distance, not linearly — doubling the distance cuts illuminance to one quarter.

Common mistakes

  • Treating lumens and lux as interchangeable: lumens describe total output regardless of distance or spread; lux describes brightness on a specific surface at a specific distance — the same bulb can register very different lux readings depending on how far away and how focused the beam is.
  • Ignoring beam angle: without a beam angle (or an illuminated area), lumens cannot be converted to lux or candela — a 1000-lumen wide floodlight and a 1000-lumen tight spotlight produce very different illuminance at the same distance.
  • Mixing distance units: keep the beam angle in degrees and convert distance to a single consistent unit before comparing results across products or spec sheets.

Real-world applications

  • Choosing flashlights, headlamps, or spotlights that deliver enough lux at the working distance you need — a trail three meters ahead versus a ceiling thirty meters up.
  • Checking that indoor lighting meets workplace or building-code illuminance targets, such as roughly 300–500 lux on an office desk.
  • Photography and videography, where candela and lux ratings help match key lights, fill lights, and reflectors to a target exposure.
  • Horticultural and aquarium lighting, where estimated lux at plant or tank height helps judge whether a fixture is bright enough.

Frequently Asked Questions

What is the difference between lumens, lux, and candela?
Lumens (lm) measure total luminous flux, the total quantity of visible light a source emits in all directions. Candela (cd) measures luminous intensity, the flux emitted per unit solid angle in a specific direction. Lux (lx) measures illuminance, the luminous flux landing on a surface per unit area (1 lux = 1 lumen per square meter).
How do you convert lumens to lux?
You can't convert lumens to lux directly without knowing the beam angle and distance (or the illuminated area). First divide lumens by the beam's solid angle to get candela (I = Φ / Ω), then divide candela by distance squared to get lux (E = I / d²), following the inverse-square law.
How is luminous intensity in candela calculated from lumens?
Luminous intensity equals luminous flux divided by the solid angle the light is spread over: I = Φ / Ω. The solid angle of a cone with full beam angle θ is Ω = 2π(1 − cos(θ/2)) steradians, so a narrower beam concentrates the same lumens into fewer steradians and produces a higher candela rating.
What are typical lux levels for common lighting situations?
Roughly: full daylight is about 10,000-25,000 lux, an overcast day is around 1,000 lux, a well-lit office desk is 300-500 lux, a living room is 100-300 lux, and a full moon at night is under 1 lux. Use these as sanity checks when comparing a calculated illuminance value to real-world expectations.

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