Case 1
- Radius (m)
- 695700000m
- Surface temperature (K)
- 5772K
0.999998L☉
Open with these valuesLuminosity Calculator
0.999998L☉
Result: 0.999998 L☉Luminosity here is a power in watts — everything a star radiates per second, not lumens. Treat the star as a blackbody sphere: L = 4π × R² × σ × T⁴. The result is shown in solar luminosities, where 1 L☉ = 3.828 × 10²⁶ W. Temperature dominates: double it and the star gets 16 times brighter.
Worked examples
Case 2
- Radius (m)
- 700000000m
- Surface temperature (K)
- 3500K
0.136873L☉
Open with these valuesCase 3
- Radius (m)
- 2500000000m
- Surface temperature (K)
- 4000K
2.978308L☉
Open with these valuesHow it's calculated
L = 4π × R² × σ × T⁴, shown as L ÷ L☉
- StepEnter the radius in metres — the Sun is 6.957 × 10⁸ m, or 695700000.
- StepEnter the effective surface temperature in kelvin, 5772 K for the Sun.
- ResultRead the result as a multiple of the Sun's radiated power.
What this number means
Luminosity is radiated power, not how bright it looks
It is the total energy a star sends out per second, at every wavelength, measured in watts. Apparent brightness in the sky is a different quantity, because that one also depends on how far away the observer stands.
Watts, not lumens
Lumens weight light by the sensitivity of the human eye, while luminosity counts every wavelength — and a star radiates most of its power outside the visible range. Without the full spectrum the two cannot be converted into one another.
Temperature counts four times over
T enters to the fourth power and R only squared, so doubling the surface temperature multiplies the luminosity by 16 while doubling the radius multiplies it by four. A hot A-type star like Sirius A reaches 25.732924 L☉ from a radius less than twice the Sun's.
Both constants are fixed, neither is measured
σ = 5.670374419e-8 W/(m²·K⁴) has been exact since the 2019 SI revision, and 1 L☉ = 3.828e26 W is the nominal value set by IAU resolution B3 of 2015. That rounded yardstick is why the Sun itself comes out at 0.999998 instead of exactly 1.
Commonly misread
Entering 1 for the Sun's radius, thinking in solar radii.
The radius box is in metres, so the Sun goes in as 695700000. A radius of 1 m at 5772 K returns 2.06611723851e-18 L☉.
Using a colour temperature from a lamp's data sheet.
The formula wants the star's effective surface temperature in kelvin, 5772 K for the Sun. A colour temperature describes the tint of a lamp, not a radiating stellar surface.
Expecting the Sun to come out at exactly 1.000000 L☉.
It gives 0.999998, because the IAU fixed the yardstick at a round 3.828e26 W while the formula returns 3.8279909e26 W. The gap sits in the sixth digit and is a matter of definition, not of error.
Reference table
| Radius (m), temperature (K) | Kind of star | L ÷ L☉ |
|---|---|---|
| 700000000, 3500 | A cool red dwarf-sized sphere | 0.136873 |
| 500000000, 4500 | A small orange main-sequence star | 0.190827 |
| 695700000, 5772 | The Sun — the yardstick itself | 0.999998 |
| 2500000000, 4000 | A cool giant | 2.978308 |
| 1190000000, 9940 | A hot A-type star like Sirius A | 25.732924 |
Questions
How do I calculate the luminosity of a star?
Treat the star as a blackbody sphere and use L = 4π × R² × σ × T⁴, with R in metres, T in kelvin and σ the Stefan-Boltzmann constant. In SI units that gives the luminosity in watts. The Sun, at 6.957 × 10⁸ m and 5772 K, comes to about 3.83 × 10²⁶ W.
What is luminosity?
It is the total energy a star radiates per second in all directions and at all wavelengths, measured in watts. Unlike apparent brightness it does not depend on how far away the observer is. Astronomers usually quote it in solar luminosities, which is what this calculator shows.
Is luminosity the same as lumens?
No. Lumens weight light by the sensitivity of the human eye, while luminosity counts every wavelength, most of which a star emits outside the visible range. The two are not interconvertible without knowing the full spectrum.
What is a solar luminosity?
It is the Sun's total radiated power, used as a yardstick for other stars. The IAU nominal value is 3.828 × 10²⁶ W. A star at 100 L☉ radiates a hundred times the Sun's power.
Why does temperature matter so much?
Because it enters to the fourth power. Doubling the surface temperature multiplies the luminosity by 16, while doubling the radius only multiplies it by four. That is why a hot blue star outshines a cooler one of the same size many times over.
Does this work for real stars?
It models the star as an ideal blackbody with emissivity 1, which is an excellent approximation because stellar surfaces radiate very close to a blackbody. Enter the effective temperature, not a colour temperature from a lamp specification. Real stars deviate slightly, but this is the standard estimate.
Sources and last check
Information, not professional advice.