Enter any two values—luminous flux (lumens), target illuminance (lux = lm/m²), or distance—into the Optical Distance Calculator. The calculator estimates the missing value using the inverse-square relationship (with assumptions noted in each tab).
Optical Distance Formula
D = SQRT (Φ / (Ω·E))
- D = distance (m)
- Φ = luminous flux (lm)
- E = illuminance (lux = lm/m²)
- Ω = solid angle (sr); isotropic point source: Ω = 4π sr; conical beam: Ω = 2π(1 − cos(θ/2))
The inverse-square law governs this relationship: luminous flux from a point source spreads across a sphere of area 4πD², so illuminance falls proportionally to 1/D². Doubling the distance reduces illuminance to one-quarter; halving it quadruples it.
Distance to Common Illuminance Thresholds by Light Source
The table below shows calculated distances at which common light sources deliver three key illuminance levels, using the isotropic point-source model (Ω = 4π). Directional fixtures with narrow beam angles achieve significantly greater distances within their beam cone.
| Light Source | Lumens | 500 lux (office task) | 100 lux (ambient) | 1 lux (dim path) |
|---|---|---|---|---|
| Candle | 12 lm | 4 cm | 10 cm | 98 cm |
| LED night light | 80 lm | 11 cm | 25 cm | 2.5 m |
| LED bulb (60W equiv) | 800 lm | 36 cm | 80 cm | 8.0 m |
| LED bulb (100W equiv) | 1,600 lm | 50 cm | 1.1 m | 11.3 m |
| Flashlight (1,000 lm) | 1,000 lm | 40 cm | 89 cm | 8.9 m |
| LED flood (5,000 lm) | 5,000 lm | 89 cm | 2.0 m | 19.9 m |
| High-bay LED | 10,000 lm | 1.3 m | 2.8 m | 28.2 m |
| LED streetlight | 20,000 lm | 1.8 m | 4.0 m | 39.9 m |
| Stadium floodlight | 100,000 lm | 4.0 m | 8.9 m | 89.2 m |
Beam angle dramatically extends throw distance. A 1,000 lm flashlight operating in an isotropic model reaches 500 lux at 40 cm. The same fixture with a 10° spot beam (Ω ≈ 0.024 sr) achieves 500 lux at 9.1 m — roughly 23 times farther — because all output concentrates into a narrow cone.
Illuminance Standards by Application (EN 12464-1)
| Application | Target Illuminance (lux) | Standard |
|---|---|---|
| Outdoor footpath (night) | 10–20 | EN 13201 |
| Residential corridor / stairway | 50–100 | EN 12464-1 |
| Living room (ambient) | 100–200 | General practice |
| Kitchen, general | 200–300 | EN 12464-1 |
| Office / classroom | 300–500 | EN 12464-1 |
| Workshop / assembly | 500–750 | EN 12464-1 |
| Technical drawing / inspection | 750–1,000 | EN 12464-1 |
| Surgical / fine inspection | 1,000–2,000 | EN 12464-1 |
Worked Examples
Example 1 — Pendant height over a kitchen counter
A 1,600 lm LED bulb needs to deliver 300 lux (kitchen task level) at the counter surface. Using D = SQRT(1600 / (4π × 300)) = SQRT(0.424) = 0.65 m. A pendant positioned 65 cm above the counter meets the target. At a typical ceiling height of 1.2 m above the counter, the same bulb yields only 88 lux — confirming why pendant and under-cabinet fixtures outperform ceiling-mounted bulbs for task lighting.
Example 2 — Streetlight fixture sizing for a parking lot
Minimum parking-lot illuminance is 10 lux (EN 13201). For a 6 m mounting height: Φ = 10 × 4π × 6² = 4,524 lm. A standard 40 W LED area light (typically 4,500–5,500 lm) satisfies minimum requirements at this pole height from directly below the fixture.
