Calculator Inputs
Plotly Graph
The graph updates after each calculation and shows how radius changes when the key driving input varies around your selected value.
Formula Used
1) Stefan-Boltzmann method
R = √(L / (4πσT⁴))
Here, R is stellar radius, L is luminosity, σ is the Stefan-Boltzmann constant, and T is effective temperature.
2) Luminosity from absolute bolometric magnitude
L / L☉ = 10^((Mbol☉ - Mbol) / 2.5)
The calculator uses Mbol☉ = 4.74. After luminosity is found, it applies the same Stefan-Boltzmann equation.
3) Luminosity from observed flux and distance
L = 4πd²F
Here, d is distance and F is observed flux. The resulting luminosity is then used to compute radius.
4) Angular diameter method
R ≈ (θ × d) / 2
This small-angle approximation is useful when angular diameter and distance are known directly.
How to Use This Calculator
- Select a calculation mode based on the data you already have.
- Enter the star name for easy report labeling.
- Fill in the visible fields only for the chosen method.
- Choose decimal precision and optional uncertainty percentage.
- Click Calculate Stellar Radius to show the result above the form.
- Review the summary table, graph, and derived values.
- Use the CSV or PDF buttons to export the calculation.
Example Data Table
These examples are illustrative and rounded for readability.
| Star | Method | Key Inputs | Approximate Radius |
|---|---|---|---|
| Sun | Luminosity + Temperature | L = 1 L☉, T = 5772 K | 1.00 R☉ |
| Sirius A | Luminosity + Temperature | L = 25.4 L☉, T = 9940 K | 1.70 R☉ |
| Rigel | Luminosity + Temperature | L = 120000 L☉, T = 12100 K | 78.83 R☉ |
| Betelgeuse | Luminosity + Temperature | L = 100000 L☉, T = 3500 K | 860.04 R☉ |
FAQs
1) What is stellar radius?
Stellar radius is the distance from a star’s center to its visible surface. It is often reported in solar radii so astronomers can compare stars directly with the Sun.
2) Which method should I choose?
Use luminosity plus temperature when those values are known. Use bolometric magnitude if catalog data lists it. Use flux and distance for observational work. Use angular diameter only when direct angular measurements exist.
3) Why does temperature strongly affect radius?
The Stefan-Boltzmann law contains temperature raised to the fourth power. Small temperature changes can therefore shift the calculated radius significantly, especially for very hot stars.
4) What is absolute bolometric magnitude?
It measures a star’s total emitted energy across all wavelengths, not only visible light. That makes it useful for estimating luminosity before solving for radius.
5) Why include uncertainty?
Observational astronomy always contains measurement error. The uncertainty field quickly shows a lower and upper radius range so you can judge sensitivity without repeating every calculation manually.
6) Is the angular diameter method exact?
No. It uses the small-angle approximation, which is excellent for tiny angular sizes. For most stars, the approximation is very accurate when the angle is small.
7) Can I use watts instead of solar luminosities?
Yes. The calculator accepts luminosity in watts or solar luminosities. It converts the input internally and returns the radius in several output units.
8) Why export CSV or PDF?
CSV is useful for spreadsheets and batch reporting. PDF is better for sharing a clean summary with teachers, students, researchers, or project stakeholders.