# From lumens and beam angle to lux.

[Read on Lightshaped](https://lightshaped.com/guides/lumens-beam-angle-to-lux)

By Lightshaped

Published: 2026-09-27

Updated: 2026-11-07

A datasheet gives lumens and a beam angle; a brief asks for lux. With the inverse-square law and a little geometry you can estimate how bright a surface will be and how large the pool of light is, before you open a full calculation tool.

## Three units, three questions

| Unit | Measures | Question it answers |
| --- | --- | --- |
| Lumen (lm) | Luminous flux | How much light does the luminaire emit in total? |
| Candela (cd) | Luminous intensity | How strong is it in one direction? |
| Lux (lx) | Illuminance, lumens per square metre | How much light lands on this surface? |

The beam angle is the angle at which the intensity has fallen to 50% of the peak. The field angle, where it falls to 10%, is wider; that is roughly where the visible edge of the pool is.

## From intensity to lux

```text
E (lx) = I (cd) × cos θ ÷ d² (m)
```

Illuminance falls with the square of the distance: twice as far away is a quarter of the light. The cosine term accounts for light arriving at an angle; straight down onto the floor, cos θ is 1.

## Estimating intensity from lumens

Without a photometric file, treat the beam as a cone that holds the flux. A cone with half-angle α covers a solid angle of 2π(1 − cos α) steradians, and dividing the lumens by it gives an average intensity. Real beams are brighter in the centre and softer at the edge, so this is an estimate, not a specification.

- Example: 1,800 lm in a 45° beam. Half-angle 22.5°, solid angle 2π(1 − cos 22.5°) ≈ 0.48 sr.
- Average intensity ≈ 1,800 ÷ 0.48 ≈ 3,750 cd.
- At 3 m straight down: 3,750 ÷ 3² ≈ 415 lx in the centre of the pool.

## How big is the pool?

```text
diameter = 2 × d × tan( beam angle ÷ 2 )
```

At 3 m a 45° beam makes a pool about 2.5 m across; a 15° beam makes one about 0.8 m across and is correspondingly much brighter in the middle. Narrow optics accent, wide optics wash.

## Uniformity and targets

Average lux is only half of the story. Uniformity, the minimum divided by the average (U0), tells you whether a space feels evenly lit or patchy. Standards such as EN 12464-1 set both an illuminance and a uniformity for each task; decorative and architectural lighting is usually judged by eye against the brief.

## When an estimate is not enough

For sign-off, use the manufacturer's IES (LM-63) or EULUMDAT file in a calculation tool such as DIALux or Relux, which also accounts for reflections from walls and ceiling. The estimate above omits reflected light and assumes uniform intensity inside the beam. Use the manufacturer’s photometric distribution for the actual shape and intensity of the beam.

## How Lightshaped does it

Lightshaped's light study uses the best source it has for each fixture: an attached IES file, datasheet lumens and beam angle, the product's published delivered lumens and optic, or a clearly labelled estimate. It computes direct illuminance on the floor or a work plane with object shadows, and the 3D preview draws its pools of light from the same numbers. It is a design aid and says so; it is not a compliance calculation.

## Questions people ask

### How do I convert lumens to lux?

Divide the lumens that reach a surface by its area in square metres. For a spotlight, estimate the intensity from lumens and beam angle, then divide by the distance squared.

### What is the difference between beam angle and field angle?

The beam angle is where intensity drops to 50% of the peak; the field angle is where it drops to 10%. The field angle is wider and closer to the visible edge of the light.

### Why is my measured lux higher than the calculation?

Simple calculations count only direct light. Light reflected from walls, ceiling and floor adds to what a meter measures in a real room.

## Sources

- [Illuminating Engineering Society: inverse-square law](https://ies.org/definitions/inverse-square-law/)
- [Illuminating Engineering Society: luminous intensity](https://www.ies.org/definitions/luminous-intensity/)

## Related guides

- [How many DMX universes does a pixel installation need?](https://lightshaped.com/guides/dmx-universes-for-pixel-installations)
- [Importing the lighting that is already in the BIM model.](https://lightshaped.com/guides/bim-ifc-lighting-import)