Main-Sequence Star Lifetime Calculator

Background.

A star's main-sequence lifetime is set by a tug-of-war between two quantities that both grow with mass. The fuel supply is proportional to the mass; the rate at which the star burns it — its luminosity — grows much faster than the mass. Divide one by the other and the lifetime shrinks steeply as stars get heavier. That is why the Sun has roughly ten billion years on the main sequence while a ten-solar-mass star has about thirty-three million: ten times the fuel, but 3162 times the burn rate, so 316 times less time.

This calculator implements the nuclear timescale, t = εfMc²/L, with a power-law mass–luminosity relation L/L☉ = (M/M☉)^α. It runs in both directions: enter a mass and get a lifetime, or enter a lifetime and get the mass that lives that long.

**None of this is exact, and the page is built so you can see exactly how inexact.** Unlike the Schwarzschild pages elsewhere in this section, every ingredient here is a fit or a modelling choice, so all three are exposed as labelled, editable inputs rather than hidden constants. The exponent α is the big one. The conventional 3.5 is a coarse average quoted for roughly 2 to 20 solar masses. Eker and colleagues (2018) fitted 509 main-sequence components of detached eclipsing binaries and found the exponent is not constant at all: 2.028 below 0.45 M☉, rising to 5.743 between 0.72 and 1.05 M☉, then falling through 4.329, 3.967 and 2.865 as mass climbs to 31 M☉. The calculator tells you which of those values applies to the mass you entered, so you can compare it with what you are using. Outside 0.179–31 M☉ there is no empirically calibrated relation at all, and the page says so rather than quietly extrapolating.

The other two parameters are the core fuel fraction f and the hydrogen-burning efficiency ε. The lifetime is exactly proportional to each of them, so a factor-of-two disagreement about f is a factor-of-two disagreement about the answer. The standard textbook f = 0.1 says a star burns about a tenth of its mass in the core before leaving the main sequence; the real value depends on how large the convective core is, which depends on mass and metallicity. For ε, AME2020 atomic masses give a mass defect of 0.0071185 for 4 ¹H → ⁴He, but about 2% of that energy leaves as neutrinos and never heats the star, leaving roughly 0.006976 thermally available. The default 0.007 is the conventional rounded value and sits between the two.

What the model ignores is as important as what it includes. It assumes the star shines at a constant luminosity for its whole main-sequence life — real stars brighten as they go, and the Sun is about 30% brighter now than it was on the zero-age main sequence. It ignores mass loss, rotation, convective-core overshoot and metallicity except through whatever numbers you type in. It cannot tell you anything about post-main-sequence evolution. Read the output as a scaling law that gets the exponent right and the prefactor approximately, not as a stellar-evolution code.

One calibration that shows the honest size of the uncertainty. The Hipparcos parallax survey dates the Hyades cluster at 625 ± 50 million years (Perryman et al. 1998). Ask this calculator which mass lives exactly 0.625 Gyr and the answer depends heavily on the exponent you chose: 3.074 M☉ with the textbook α = 3.5, 2.549 M☉ with α = 4.0, and 2.324 M☉ with Eker's measured α = 4.329 for that mass range. A 24% change in the exponent moves the answer by 32%. That spread is the honest precision of this method, and it is the reason the exponent is a field you can edit rather than a number baked into the code.

What is star lifetime calculator?

The main sequence is the long, stable phase in which a star fuses hydrogen to helium in its core, and it accounts for roughly 90% of a typical star's luminous life. Its duration is the nuclear timescale: the energy available divided by the rate it is spent.

The energy available is εfMc². M is the star's mass, f is the fraction of that mass that actually passes through the core reactions, and ε is the fraction of rest mass that fusion converts to energy — about 0.7% for hydrogen to helium, which is why stars last so long compared with anything chemical. The rate it is spent is the luminosity L, and for main-sequence stars L rises steeply with mass, roughly as a power law.

Putting those together, t ∝ M/L ∝ M^(1−α). With α greater than 1, the exponent is negative and heavier stars live shorter lives. With the conventional α = 3.5 the scaling is t ∝ M^−2.5, so a star ten times the Sun's mass lives about 1/316 as long.

The mass–luminosity relation itself is empirical. It was first mapped by Eddington in the 1920s and has been recalibrated many times since, most comprehensively from detached eclipsing binaries, which give masses and radii directly rather than through a model. It is not a single power law across the whole main sequence, and this page makes the exponent your choice for that reason.

What this is not: it is not a stellar-evolution model, it does not track how the star's structure changes, it says nothing about what happens after the main sequence, and it cannot be used to date an individual star from its present appearance. It answers one question — how long does hydrogen core burning last — under stated assumptions.

How to use this calculator.

1. 01Choose the forward route (mass → lifetime) or the inverse (lifetime → mass).
2. 02Enter the stellar mass in solar masses, or the lifetime in billions of years.
3. 03Check the mass–luminosity exponent. 3.5 is the conventional value for 2–20 M☉; the result note tells you what Eker et al. (2018) measured for the mass you entered, and changing α is by far the biggest lever on the answer.
4. 04Adjust the core fuel fraction if you have a better value than the standard 0.1. The lifetime is exactly proportional to it.
5. 05Adjust the hydrogen-burning efficiency if you want the raw AME2020 mass defect (0.0071185) or the neutrino-corrected value (0.006976) instead of the conventional 0.007.
6. 06Read the lifetime, and read the lifetime-relative-to-the-Sun figure alongside it — that ratio depends only on mass and α, so it is the most robust number on the page.
7. 07Read the model note before quoting anything. It states the constant-luminosity assumption and warns if your mass falls outside the calibrated range.

The formula.

The nuclear timescale is a two-line argument. The energy a star can release from core hydrogen burning is E = ε f M c², where f is the fraction of the star's mass that passes through the core reactions and ε is the fraction of rest mass fusion converts. Dividing by the rate at which the star radiates gives the time it can keep doing so: t = ε f M c² / L. Substituting the power-law mass–luminosity relation L = L☉(M/M☉)^α and collecting terms 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. Inverting that gives M = (t/K)^(1/(1−α)).

With the default numbers, K works out to ε f M☉ c²/L☉ = 0.007 × 0.1 × 1.98841 × 10³⁰ × 8.987551787 × 10¹⁶ / 3.828 × 10²⁶ = 3.26794 × 10¹⁷ seconds, which is 10.355 billion years. Every other answer on the page is that number multiplied by (M/M☉)^(1−α).

Units and dimensions. Mass is entered in solar masses and reported also in kilograms; luminosity in solar luminosities and watts; lifetime in Julian years of exactly 31 557 600 s and in Gyr. The exponent, the fuel fraction, the efficiency and the lifetime-relative-to-the-Sun ratio are all dimensionless. The dimensional guard the test suite runs is that the returned energy reservoir in joules, divided by the returned luminosity in watts, reproduces the returned lifetime in seconds — J/W = s, with no constants left over.

Rounding stage. No intermediate rounding: forty significant digits throughout, rounded once at the return boundary to twelve significant digits. Decimal-place rounding was rejected because the outputs span an enormous range — a 0.08 M☉ star gets 10⁴ Gyr and a 150 M☉ star gets 10⁻⁵ Gyr, and the energy reservoir is around 10⁴⁴ joules.

Significant figures. Two, at most. The page returns twelve digits so that ratios and round-trips are checkable, but the physics does not support more than about one significant figure: the fuel fraction alone is uncertain at the tens-of-per-cent level, and the exponent choice moves the answer by more than that.

Invalid-domain behaviour. Zero or negative mass, zero or negative lifetime, a non-positive exponent, a fuel fraction outside (0, 1] and an efficiency outside (0, 1) each raise their own field error. One case is a genuine mathematical singularity rather than a guard: **an exponent of exactly 1 makes the lifetime independent of mass**, because t ∝ M^(1−α) = M⁰, so the inverse M = (t/K)^(1/(1−α)) has no solution and the page raises an error explaining why. Near that pole the inverse runs away — at α = 0.9 a 5 Gyr lifetime implies 0.000689 M☉ and at α = 1.1 it implies 1452 M☉ — and if it runs away far enough to overflow double precision the calculator refuses rather than returning Infinity. Two mass thresholds attach notes rather than errors: outside 2–20 M☉ the conventional single exponent is flagged as out of its usual band, and outside 0.179–31 M☉ the page warns that no empirically calibrated mass–luminosity relation covers the mass at all.

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.