Measure critical luminosity from mass and opacity inputs. Review accretion rates and compare observed brightness. Use straightforward fields, exports, tables, formula notes, and FAQs.
Eddington luminosity: LEdd = 4πGMc / κ
Eddington accretion rate: ṀEdd = LEdd / (ηc²)
Eddington ratio: λ = Lobs / LEdd
Here, G is the gravitational constant, M is object mass, c is the speed of light, κ is opacity, and η is radiative efficiency.
| Object | Mass (M☉) | κ (m²/kg) | Observed Luminosity (W) | L_Edd (W) | Eddington Ratio |
|---|---|---|---|---|---|
| Sun-like Star | 1 | 0.034 | 1.000000e+31 | 1.470539e+31 | 0.680023 |
| Stellar Black Hole | 10 | 0.034 | 5.000000e+31 | 1.470539e+32 | 0.340011 |
| Quasar Engine | 100000000 | 0.034 | 8.000000e+38 | 1.470539e+39 | 0.543989 |
Eddington luminosity is the maximum steady radiative output that a luminous body can sustain when outward radiation pressure balances inward gravity. This idea is central in stellar structure, compact objects, black hole accretion, and quasar studies. It helps astrophysicists test whether an object radiates calmly, approaches instability, or enters a super-Eddington state.
This calculator estimates the Eddington luminosity from mass and opacity. Mass controls gravitational pull. Opacity controls how strongly matter interacts with radiation. A lower opacity allows more luminosity before radiation pressure wins. A higher opacity lowers the permitted radiative ceiling. The tool also estimates the Eddington accretion rate from radiative efficiency, which is useful for black hole growth models.
Observed luminosity adds context. When you enter measured luminosity, the calculator finds the Eddington ratio. This ratio is widely used in high energy astrophysics. Values below one indicate sub-Eddington flow. Values near one suggest strong radiation feedback. Values above one can indicate anisotropic emission, beaming, photon trapping, or genuinely super-Eddington accretion.
Mass scaling is simple. If opacity stays fixed, the Eddington luminosity rises linearly with mass. A ten-solar-mass object has ten times the limit of a one-solar-mass object. This makes comparison easy across stellar remnants and active galactic nuclei. The calculator shows that scaling clearly through luminosity per solar mass.
You can use this page for stars, X-ray binaries, neutron stars, active galactic nuclei, and quasars. It is also helpful for classroom work, quick checks, and article drafting. Because the result is shown in watts, erg per second, and solar luminosities, you can compare outputs across common astronomy conventions without extra conversions.
The Eddington limit is a model, not a final verdict. Real systems may depart from ideal spherical symmetry. Magnetic fields, changing opacity, disk geometry, and composition all matter. Distance errors and band-limited observations can also shift inferred luminosity. Use this calculator as a strong physical benchmark, then compare with detailed source models and measured spectra.
It is the theoretical luminosity where outward radiation pressure balances inward gravitational pull in ionized matter. Above this level, steady spherical inflow becomes difficult to maintain.
Opacity controls how effectively radiation pushes on matter. Larger opacity means stronger radiation pressure for the same luminosity, so the Eddington limit becomes lower.
Use ionized hydrogen for simple electron scattering cases, solar composition for mixed plasma approximations, helium for helium-rich matter, or custom when your model provides κ directly.
It is the observed luminosity divided by the Eddington luminosity. It quickly shows whether a source is comfortably below the limit, close to it, or above it.
Radiative efficiency converts luminosity into an accretion rate estimate. It tells the calculator how much emitted energy is produced per unit rest mass energy accreted.
Yes. It is useful for stellar black holes and supermassive black holes. It is especially handy when you want a quick benchmark for accretion-powered luminosity.
No. Some sources can appear or remain super-Eddington because of disk geometry, beaming, time variability, photon trapping, or nonuniform outflows.
Astronomy papers use watts, erg per second, and solar luminosities. Showing all three makes comparison easier across textbooks, observations, and research articles.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.