Apparent magnitude to watts per square meter
Type a value in mag to get it in W/m² instantly.
1.002×10⁻¹⁰W/m²
That's 41× as bright as Polaris, while the naked-eye limit is 1.58× fainter. That is bright enough to see with the naked eye from a dark site.
What it means
How bright is that?
These are apparent magnitudes: how bright something looks from Earth, not how much light it truly gives out.
The math
How to convert mag to W/m²
Magnitude is logarithmic and inverted: m = −2.5 × log₁₀(brightness ratio), and back again ratio = 10^(−m ÷ 2.5). Five magnitudes is exactly a hundredfold.
Example: 6 mag = 1.002×10⁻¹⁰ W/m².
Every unit
Your brightness in every unit
Tables
mag to W/m² conversion table
| mag | W/m² |
|---|---|
| -26 mag | 632.493 W/m² |
| -12 mag | 0.00158875 W/m² |
| -4 mag | 1.002×10⁻⁶ W/m² |
| -1 mag | 6.325×10⁻⁸ W/m² |
| 0 mag | 2.518×10⁻⁸ W/m² |
| 1 mag | 1.002×10⁻⁸ W/m² |
| 3 mag | 1.589×10⁻⁹ W/m² |
| 6 mag | 1.002×10⁻¹⁰ W/m² |
| 10 mag | 2.518×10⁻¹² W/m² |
| 15 mag | 2.518×10⁻¹⁴ W/m² |
| 20 mag | 2.518×10⁻¹⁶ W/m² |
| 25 mag | 2.518×10⁻¹⁸ W/m² |
W/m² to mag conversion table
| W/m² | mag |
|---|---|
| 2.52×10⁻¹⁸ W/m² | 24.9991 mag |
| 2.52×10⁻¹⁶ W/m² | 19.9991 mag |
| 2.52×10⁻¹⁴ W/m² | 14.9991 mag |
| 2.52×10⁻¹² W/m² | 9.99914 mag |
| 1×10⁻¹⁰ W/m² | 6.00264 mag |
| 1.59×10⁻⁹ W/m² | 2.99915 mag |
| 1×10⁻⁸ W/m² | 1.00264 mag |
| 2.52×10⁻⁸ W/m² | -0.000862038 mag |
| 6.32×10⁻⁸ W/m² | -0.999153 mag |
| 1×10⁻⁶ W/m² | -3.99736 mag |
| 0.00159 W/m² | -12.0009 mag |
| 632 W/m² | -25.9992 mag |
Quick answers
Quick answers
- How many W/m² is 1 mag?
- 1 mag is 1.002×10⁻⁸ W/m².
- How many W/m² is 10 mag?
- 10 mag is 2.518×10⁻¹² W/m².
- How many W/m² is 6 mag?
- 6 mag is 1.002×10⁻¹⁰ W/m².
The units
About these units
Apparent magnitude (mag)
The astronomer’s brightness scale, running backwards from bright to faint.
Watts per square meter (W/m²)
The actual energy arriving from it across the visible band.
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