Case 1
- Luminosity
- 1W
- Distance
- 1m
0.079577W/m²
Open with these valuesApparent Brightness Calculator
0.079577W/m²
Result: 0.079577 W/m²All the power a source radiates ends up spread over a sphere, so the flux you receive is the luminosity divided by 4π times the distance squared. Double the distance and the brightness drops to a quarter. Nothing here accounts for dust or haze along the way.
Worked examples
Case 2
- Luminosity
- 100W
- Distance
- 2m
1.989437W/m²
Open with these valuesCase 3
- Luminosity
- 1000W
- Distance
- 10m
0.795775W/m²
Open with these valuesHow it's calculated
b = L ÷ (4 × π × d²)
- StepEnter the source's total radiated power in watts.
- StepEnter your distance from it in metres.
- ResultRead the flux arriving on one square metre.
Reference table
| Luminosity, distance | In words | Flux (W/m²) |
|---|---|---|
| 1, 1 | One watt, one metre away | 0.079577 |
| 100, 2 | 100 W at two metres | 1.989437 |
| 1000, 10 | 1 kW at ten metres | 0.795775 |
| 60, 3 | A 60 W lamp across the room | 0.530516 |
| 1000, 100 | The same kilowatt, ten times further | 0.007958 |
Questions
Why divide by 4π?
A point source radiates in every direction, so its power spreads over a whole sphere. The surface of a sphere of radius d is 4πd², and the flux is the power per unit of that surface.
What happens when I double the distance?
The brightness falls to one quarter. The same 1 kW gives 0.795775 W/m² at ten metres and 0.007958 W/m² at a hundred.
Does this include absorption on the way?
No. The formula describes empty space; dust, haze or atmosphere only take more away, so a real measurement comes out lower.
Is this the same as apparent magnitude?
No. Magnitude is a logarithmic scale built on top of a flux like this one, not the flux itself.
Sources and last check
Information, not professional advice.