PhysicsCalcs
Optics

Lumen Calculator

Convert between lumens, lux, candela, and footcandles. Calculate illumination at distance and light source requirements.

Interactive calculator

Lumen Calculator

Convert between lumens, lux, candela, and footcandles. Calculate illumination at distance, beam angle effects, and light source requirements.

Try an example

Your result will appear here.

Choose a calculation mode, fill in the known values, and click Calculate.

Quick Guide

  • Choose: lumens ↔ lux, candela ↔ lumens, lux ↔ candela, or illumination at distance.
  • Use presets for LED bulbs, flashlights, stage lights.
  • Click Calculate for results with footcandle conversion.

Table of Contents

Key Takeaways

  • Lumens (lm) measure total light output; lux (lx) measures light per unit area; candela (cd) measures directional intensity.
  • 1 lux = 1 lumen per square metre = 0.0929 footcandles.
  • Illuminance follows the inverse-square law: doubling distance quarters the lux.
  • Beam angle determines how lumens are concentrated — narrower beams give higher candela.
  • LED efficacy (100-200 lm/W) far exceeds incandescent (15 lm/W).

Lumens, Lux & Candela

These three photometric units describe different aspects of light. Lumens measure total visible light output. Lux measures how much light falls on a surface. Candela measures directional intensity. Understanding these relationships is key for lighting design, photography, and display engineering.

Key Formulas

E=ΦA[lux=lm/m2]E = \frac{\Phi}{A} \quad [\text{lux} = \text{lm/m}^2]
Φ=I⋅Ω,Ω=2π(1−cos⁡α)\Phi = I \cdot \Omega, \quad \Omega = 2\pi(1 - \cos\alpha)
E=Id2(inverse-square law)E = \frac{I}{d^2} \quad \text{(inverse-square law)}

Where Φ is luminous flux (lumens), E is illuminance (lux), I is luminous intensity (candela), A is area, Ω is solid angle, α is half-beam angle, and d is distance.

Lighting Guidelines

SpaceLuxFootcandles
Hallway50–1005–10
Living room100–30010–30
Office300–50030–50
Kitchen300–75030–70
Detailed work500–100050–100
Surgery10000–1000001000–10000

Luminous Efficacy

SourceEfficacy (lm/W)Typical lumens
Incandescent10–17800 lm (60W)
Halogen15–25800 lm (43W)
CFL50–70800 lm (13W)
LED100–200800 lm (8W)

How to Use

  1. Select a conversion mode from the dropdown.
  2. Enter known values (lumens, lux, candela, area, distance, or beam angle).
  3. Click Calculate for results with footcandle conversion.

Examples

800 lm LED in 10 m² room

E = 800 / 10 = 80 lux (suitable for a hallway, add more for an office)

Flashlight (1000 lm, 10° beam)

cd = 1000 / (2π(1 − cos 5°)) ≈ 41,700 cd

Office lighting (400 lux, 20 m²)

Required lumens = 400 × 20 = 8,000 lm (≈ 10 LED bulbs at 800 lm)

FAQ

What is the difference between lumens, lux, and candela?›

Lumens measure total light output from a source. Lux measures how much light hits a surface (lumens per m²). Candela measures light intensity in a specific direction. An 800 lm bulb with a narrow beam has high candela but the same lumens as a wide-beam bulb.

How many lumens do I need for a room?›

General guidelines: living room 100-300 lux, office/kitchen 300-500 lux, detailed work 500-1000 lux. Multiply by floor area (m²) to get required lumens. A 20 m² office at 400 lux needs 8,000 lumens total.

What are footcandles?›

Footcandles (fc) are the imperial unit of illuminance: 1 fc = 1 lumen per square foot ≈ 10.764 lux. They're still used in North American lighting standards, especially for architectural and building codes.

How does beam angle affect illumination?›

A narrower beam concentrates the same lumens into a smaller area, increasing both candela (intensity) and lux at the target. A 10° flashlight beam is much brighter than a 120° room light, even with the same lumens.

What is luminous efficacy?›

Luminous efficacy (lm/W) measures how efficiently a source converts electrical power to visible light. Modern LEDs: 100-200 lm/W, CFL: 50-70 lm/W, halogen: 15-25 lm/W, incandescent: 10-17 lm/W.

Sources

  1. IES Lighting Handbook
  2. Wikipedia – Lumen (unit)
  3. HyperPhysics – Photometry
Manish Kumar

Author & technical reviewer

Manish Kumar

PhysicsCalcs tools are reviewed with an educational focus: clear formulas, transparent assumptions, and practical context for students and science learners.

Learn more about Manish