Candela to Lumens Converter
Candela to lumens and back from a beam angle: lm = cd × 2π(1 − cos(θ/2)). 1,000 cd in a 60° beam is 841.8 lm. Angles up to 180°. How it works
Use the Candela to Lumens Converter
About the Candela to Lumens Converter
Lumens = candela × 2π(1 − cos(θ/2)), where θ is the full beam angle, and candela = lumens ÷ 2π(1 − cos(θ/2)). A 500 lm bulb with a 36° beam has a solid angle of 0.3075 sr, so its peak intensity is about 1,625.9 cd. The result is an estimate that treats the beam as an even cone of light with a sharp edge. Lux mode gives the light landing on a surface: lux = cd ÷ d², so 100 cd at 2 m is 25 lx, 2.3226 foot-candles.
Candela to lumens by beam angle
| Beam angle | Solid angle (sr) | Lumens from 1,000 cd | Candela from 1,000 lm |
|---|---|---|---|
| 10° | 0.0239 | 23.9094 | 41824.5246 |
| 15° | 0.0538 | 53.7535 | 18603.4324 |
| 25° | 0.1489 | 148.9366 | 6714.2673 |
| 36° | 0.3075 | 307.5210 | 3251.8107 |
| 60° | 0.8418 | 841.7872 | 1187.9487 |
| 90° | 1.8403 | 1840.3024 | 543.3890 |
| 120° | 3.1416 | 3141.5927 | 318.3099 |
| 180° | 6.2832 | 6283.1853 | 159.1549 |
Values as the converter shows them, to four decimal places. For other amounts, scale in proportion: 2,000 cd at 60° is twice 841.7872 lm.
Supported inputs
- Value: 0 or more, in candela or lumens depending on the direction
- Beam angle: above 0 and up to 180 degrees (the slider runs from 1 to 180 degrees)
- Lux mode: a distance above 0 in meters or feet, or an area above 0 in m² or ft²
Supported outputs
- Lumens or candela, to four decimal places
- Solid angle of the beam in steradians, to four decimal places
- Lux and foot-candles, to four decimal places, in Lux mode
Methodology
The beam angle θ is the full angle of the cone, not the half-angle. It is turned into a solid angle Ω = 2π(1 − cos(θ/2)) sr, then lumens = candela × Ω and candela = lumens ÷ Ω, since 1 lm is 1 cd·sr. 4π sr is the solid angle of a full sphere; 2π sr is a hemisphere, which is the 180° limit of the input. Lux mode uses the inverse-square law for a surface facing the lamp, lux = cd ÷ d² with d in meters, or lux = lm ÷ area in m², and foot-candles = lux ÷ 10.7639 (1 ft² = 0.09290304 m²).
Assumptions
- Intensity is taken as the same everywhere inside the cone and zero outside it. Real beams fade toward the edge, so the result is an estimate, not a measurement.
- Spec sheets usually give the beam angle at half of the peak intensity (the IES definition), and some light falls outside that angle, so a fixture’s rated lumens are often higher than this tool’s figure for its peak candela.
- Angles above 180° are not accepted. For a bulb that shines evenly in every direction, use the full sphere by hand: lumens = candela × 4π, about candela × 12.566.
How to use this tool
- Choose Candela → Lumens or Lumens → Candela, or Lux for the light on a surface. The round button switches direction and empties the value box.
- Enter the value and the beam angle in degrees, or move the slider from 1° to 180°.
- Read the result to four decimal places, with the solid angle in steradians under the formula.
- In Lux mode, start from candela at a distance, lumens in a beam at a distance, or lumens over an area, and read lux with foot-candles beside it.
Frequently asked questions
- What is the difference between candela and lumens?
- Lumens count all the visible light a source puts out. Candela is how strong that light is in one direction, in lumens per steradian. A flashlight and a bare bulb can have the same lumens while the flashlight has many times the candela, because it packs the light into a narrow beam.
- How many lumens is 1 candela?
- It depends on the beam. 1 cd spread evenly over a full sphere is 4π, about 12.57 lm. Over a hemisphere (180° here) it is 6.2832 lm, and in a 60° cone it is 0.8418 lm.
- Does a narrower beam mean more candela?
- Yes, for the same lumens. 1,000 lm in a 60° beam is 1,187.9 cd, and squeezed into 15° it is 18,603.4 cd. Turned the other way, the same candela in a narrower beam means fewer lumens.
- Why does my result not match the spec sheet?
- Spec sheets measure the real beam, which fades toward its edge and spills some light outside the stated beam angle. This tool assumes an even cone with a hard edge, so expect a difference. Treat the result as a rough check.
- Can it convert candela or lumens to lux and foot-candles?
- Yes, in Lux mode. Lux is lumens per square meter landing on a surface, so it depends on the distance. From candela, lux = cd ÷ d²: 100 cd at 2 m is 25 lx (2.3226 fc), and 1,000 cd at 3 ft is 111.1111 fc. From a beam’s lumens the beam angle gives the candela first: 500 lm in a 36° beam at 2 m is 406.4763 lx. Lumens spread over an area: 500 lm over 10 m² is 50 lx (4.6452 fc).
Related Tools
View all toolsHalogen Wattage Converter
Convert halogen or incandescent bulb wattage to equivalent LED wattage and lumens
LED vs Incandescent Savings Calculator
LED vs incandescent cost from wattage, hours a day and electricity rate, counting replacement bulbs by rated life, with payback and CO₂ from EPA eGRID.
Hex to ASCII
Convert hex to ASCII text: 48 65 6C 6C 6F is Hello. Bytes are read as UTF-8, and odd digit counts or bad characters get an error.
Tile Calculator
Tile calculator for a floor or wall in grid, diagonal, offset or herringbone, with grout gap and waste: 10 × 10 ft of 12 in tiles is 100, or 110 with waste.
Fence Post Spacing Calculator
Fence posts from the length and a maximum spacing: posts = ceil(length ÷ spacing) + 1, spread evenly, with gates, corners, rails, pickets and concrete.
Cooking Measurement Converter
Convert cups, tbsp, tsp, fl oz and ml, grams and ounces, or turn a volume into grams for flour, sugar, butter, milk, oil, honey and water.