Main-Sequence Star Lifetime Calculator

Background.

A star ten times as massive as the Sun carries ten times as much hydrogen, yet it runs out about 300 times sooner. The reason is luminosity. Along the main sequence, brightness climbs far faster than mass: with the conventional mass–luminosity exponent of 3.5, ten solar masses shine 10^3.5, about 3,162, times as bright as the Sun. Ten times the fuel spent 3,162 times as fast leaves roughly 1/316 of the time, some 33 million years against the Sun's ten billion.

That argument is the nuclear timescale, and it runs here in either direction: from a mass to a lifetime, or from a lifetime back to the mass that lasts exactly that long. The energy on hand is a small fraction of the star's rest mass, ε f M c², and the lifetime is that energy divided by the luminosity.

Three ingredients are modelling choices rather than constants of nature, so all three are inputs. The exponent α is the sensitive one: measurements of eclipsing binaries by Eker and colleagues (2018) put it anywhere from 2.0 to 5.7 depending on the mass range, rather than a steady 3.5. The core fuel fraction f, conventionally 0.1, and the burning efficiency ε, about 0.007, each scale the answer in direct proportion.

The result is a scaling law, not a stellar-evolution model. It assumes the star shines at constant brightness, although the Sun is about 30 percent brighter today than when it began fusing hydrogen, and it leaves out mass loss, rotation and mixing beyond the core. What it captures well is the shape of the dependence, which is enough to show why the most massive stars are always young and why no red dwarf has yet had time to burn out.

What is star lifetime calculator?

The main-sequence lifetime is the time a star spends fusing hydrogen into helium in its core, the long, stable stage that takes up most of a star's life and the stage the Sun is in now. On the nuclear timescale it is the energy that core hydrogen burning can release divided by the rate at which the star radiates: t = ε f M c² / L. Because L rises roughly as a power of mass, M^α, the lifetime scales as M^(1−α), which is M^−2.5 for α = 3.5. Below about 0.08 solar masses hydrogen never ignites, so a brown dwarf has no main sequence and no lifetime in this sense.

How to use this calculator.

1. 01Under 'What do you want to find?', choose mass to lifetime for a star of known mass, or lifetime to mass to ask which star would just be leaving the main sequence after a given time, such as the age of a cluster.
2. 02Enter the mass in solar masses, or the lifetime in billions of years (Julian years of 31,557,600 s).
3. 03Set the mass–luminosity exponent. Keep 3.5 for a rough figure between about 2 and 20 solar masses; for a closer match use the Eker et al. value for your mass, which the results note quotes: 2.028 up to 0.45 M☉, 4.572 to 0.72, 5.743 to 1.05, 4.329 to 2.40, 3.967 to 7 and 2.865 to 31.
4. 04Leave the core fuel fraction at 0.1 unless you have a reason to change it. Red dwarfs below about a third of a solar mass are convective throughout and stir nearly all their hydrogen through the core, so a far larger fraction suits them.
5. 05Pick the efficiency: 0.007 by convention, 0.0071185 for the full mass defect of hydrogen-to-helium fusion, or about 0.006976 if you discount the roughly 2 percent carried off by neutrinos.
6. 06Read the lifetime relative to the Sun alongside the absolute figure. It depends only on mass and exponent, so it is unaffected by whatever you chose for f and ε.

The formula.

Fusion turns four hydrogen atoms into one helium-4 atom, and the helium is lighter. With AME2020 atomic masses the loss is (4 × 1.00782503190 − 4.00260325413) ÷ (4 × 1.00782503190) = 0.0071185 of the rest mass; that fraction is ε. If a share f of the star's mass M is burned before the star leaves the main sequence, the energy available is E = ε f M c², and dividing by the luminosity gives the time: t = ε f M c² / L.

The luminosity comes from the mass–luminosity relation L = L☉ (M/M☉)^α, with L☉ = 3.828 × 10²⁶ W, the IAU 2015 nominal value. Substituting gives t = K (M/M☉)^(1−α), where K = ε f M☉ c² / L☉ is the lifetime of a one-solar-mass star under the same assumptions. With M☉ = 1.98841 × 10³⁰ kg, ε = 0.007 and f = 0.1, K = 3.268 × 10¹⁷ s, or 10.355 billion years. The inverse route solves M = (t/K)^(1/(1−α)).

Since α sits in an exponent, small changes to it move the answer a long way, while f and ε only rescale it in proportion. At α = 1 the lifetime would be the same for every mass, so the inverse has no solution and is refused. Near α = 1 the inverse becomes wildly unstable: a 5 Gyr lifetime implies 0.000689 M☉ at α = 0.9 and 1,452 M☉ at α = 1.1.

A worked example.

Frequently asked questions.

References& sources.

1. [1]Eker, Z., et al. (2018), "Interrelated main-sequence mass–luminosity, mass–radius, and mass–effective temperature relations", Monthly Notices of the Royal Astronomical Society 479, 5491; arXiv:1807.02568, full text retrieved 2026-07-29. Uses absolute parameters of 509 main-sequence stars from detached eclipsing spectroscopic binaries. Table 4 gives the six-piece classical mass–luminosity relation L ∝ M^α with α = 2.028 (0.179–0.45 M☉), 4.572 (0.45–0.72), 5.743 (0.72–1.05), 4.329 (1.05–2.40), 3.967 (2.40–7) and 2.865 (7–31), and states that the exponent "is smallest (α=2.028) in the ultra low mass domain … then it increases and reaches its maximum (α=5.743) in the low mass domain". This is the second, independent authority: it contradicts the single conventional exponent 3.5 everywhere, which is why α is an editable input. Peer-reviewed; open-access preprint.
2. [2]Perryman, M. A. C., et al. (1998), "The Hyades: distance, structure, dynamics, and age", Astronomy & Astrophysics 331, 81; arXiv:astro-ph/9707253, abstract retrieved 2026-07-29. States a cluster age of 625 ± 50 Myr from Hipparcos astrometry. Used here only as an external calibration point for the inverse route; the turnoff MASS is deliberately not quoted, because the abstract does not give one. Peer-reviewed; open-access preprint.
3. [3]Wang, M., Huang, W. J., Kondev, F. G., Audi, G. and Naimi, S. (2021), "The AME 2020 atomic mass evaluation (II)", Chinese Physics C 45, 030003. Source of the atomic masses m(¹H) = 1.00782503190 u and m(⁴He) = 4.00260325413 u from which the hydrogen-burning efficiency ε = 0.0071185 is computed. Peer-reviewed; the evaluation and its data files are freely distributed by the AMDC. Bibliographic citation — the two mass values are standard and appear in every AME2020 mirror.
4. [4]Prša, A., et al. (2016), "Nominal Values for Selected Solar and Planetary Quantities: IAU 2015 Resolution B3", Astronomical Journal 152, 41; arXiv:1510.07674, retrieved 2026-07-29. Table 1 gives the nominal solar luminosity 3.828 × 10²⁶ W used to normalise every luminosity here, and states that these are standard conversion factors rather than current best estimates of the real Sun. Peer-reviewed; open-access preprint.
5. [5]Particle Data Group (Workman et al.), Review of Particle Physics, "Astrophysical Constants and Parameters", Table 2.1, revised August 2023; 2024 PDF retrieved 2026-07-29. Source of the solar mass M☉ = 1.98841(4) × 10³⁰ kg. Open access.
6. [6]NIST/CODATA 2022, "Speed of light in vacuum": c = 299 792 458 m s⁻¹, exact. Retrieved 2026-07-29. Standards body; open access.