What this calculator does
Lumens measure the total light a source puts out; candela measures how intensely that light is concentrated in a particular direction. The two are connected by the solid angle the light is spread across, measured in steradians, so the same lumen output produces a very different candela reading depending on whether it is spread evenly in every direction or focused into a narrow beam.
A bare bulb radiating in every direction covers the full sphere of 4π steradians, about 12.566 sr. A torch or spotlight concentrates its output into a much smaller solid angle, which is why a modest lumen rating can still produce a very high candela figure once it is focused down to a tight beam.
The formula
Divide lumens by the solid angle in steradians to get candela, or multiply candela by the solid angle to get lumens back. The default solid angle is 4π (about 12.566 sr), the full sphere used for a source that emits equally in every direction; change it to a smaller figure to model a focused beam instead.
| Term | Meaning |
|---|---|
| Lumen (lm) | The total quantity of visible light a source emits, in every direction it covers. |
| Candela (cd) | Luminous intensity in a given direction, equal to lumens divided by the solid angle they are spread over. |
| Steradian (sr) | The unit of solid angle; a full sphere is 4π sr, about 12.566 sr. |
The inputs explained
| Field | What to enter |
|---|---|
| Convert | Choose whether to convert from lumens to candela or the other way around. |
| Luminous flux (lm) | The total light output in lumens, usually taken from a product's packaging or datasheet. |
| Luminous intensity (cd) | The luminous intensity in candela, if that is the figure you already have. |
| Solid angle covered by the beam (sr) | The solid angle the light covers. Leave at 12.566 for a bulb that radiates in every direction, or enter a smaller figure for a focused beam. |
When to use it
Comparing a floodlight and a torch of similar lumens
Two lights rated at the same lumen figure can behave very differently: the floodlight spreads that output across the full sphere, while the torch concentrates it into a narrow cone, giving it a much higher candela and a longer effective throw.
Reading a torch or spotlight datasheet
Some manufacturers quote lumens, others quote candela (sometimes labelled peak beam intensity); converting between the two, once the beam angle is known or estimated, puts competing products on the same footing.
Working from a bulb rated for even coverage
A standard household bulb that emits roughly evenly in every direction uses the full 4π solid angle by default, so its lumen rating alone is enough to estimate its candela.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How candela changes as the beam is focused tighter, at 800 lumens
A fixed 800 lumens spread across solid angles from a full sphere down to a tight beam.
| Solid angle | Result |
|---|---|
| 12.566 sr | 63.7 cd |
| 1 sr | 800.0 cd |
| 0.5 sr | 1,600.0 cd |
| 0.1 sr | 8,000.0 cd |
| 0.05 sr | 16,000.0 cd |
| 0.01 sr | 80,000.0 cd |
Questions
Why does the same lumen rating give such different candela figures?
Because candela measures concentration, not total output. Spreading a fixed amount of light over a smaller solid angle increases its intensity in that direction, even though the total lumens have not changed.
What solid angle should I use for an ordinary light bulb?
The default of 4π steradians, about 12.566 sr, assumes the bulb emits fairly evenly in every direction, which is a reasonable approximation for a standard household bulb without a reflector.
How do I estimate the solid angle of a focused beam?
Manufacturers sometimes quote a beam angle in degrees rather than a solid angle directly; converting a beam angle to steradians needs its own formula, but many torch and spotlight datasheets state the beam solid angle or an equivalent candela figure directly.
Is this the same as the lumens to watts conversion?
No. Lumens to candela relates total light output to its intensity in a direction; the separate lumens to watts calculator instead estimates the electrical power a bulb needs to produce a given brightness.
For the electrical power needed to produce a given brightness, see the lumens to watts calculator.