Hertzsprung-Russell Estimator Formula

Understand the math behind the hertzsprung-russell estimator. Each variable explained with a worked example.

Use the Hertzsprung-Russell Estimator

Formulas Used

Luminosity (L_sun)

luminosity_solar = pow(temperature / 5778, 4) * pow(pow(temperature / 5778, 0.8), 2)

Radius (R_sun)

radius_solar = pow(temperature / 5778, 0.8)

Variables

VariableDescriptionDefault
temperatureEffective Temperature(K)5778

How It Works

The Hertzsprung-Russell Diagram

The HR diagram plots stellar luminosity against temperature. For main-sequence stars, hotter stars are larger and more luminous.

Empirical Approximation

Radius: R / R_sun ≈ (T / T_sun)^0.8

Luminosity from Stefan-Boltzmann: L / L_sun = (R/R_sun)² × (T/T_sun)⁴

These are rough main-sequence estimates. Giants, supergiants, and white dwarfs fall off the main sequence.

Worked Example

A star with T = 10 000 K (A-type).

temperature = 10000
  1. 01T/T_sun = 10000/5778 = 1.731
  2. 02R/R_sun ≈ 1.731^0.8 ≈ 1.562
  3. 03L/L_sun = 1.562² × 1.731⁴ = 2.440 × 8.975 ≈ 21.9
  4. 04About 22 solar luminosities.

Ready to run the numbers?

Open Hertzsprung-Russell Estimator