Chandrasekhar Limit Calculator

Find the maximum mass a white dwarf can support before electron degeneracy pressure fails and the star collapses.

💥 Chandrasekhar Limit Calculator
Mean Molecular Weight per Electron (μe)2.00
1.0 (H)3.0
White Dwarf Mass1.00 M☉
M☉
0.1 M☉3.0 M☉
Mean Molecular Weight per Electron (μe)2.00
1.03.0
Chandrasekhar Limit
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Mass in kg
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Composition Regime
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Chandrasekhar Limit
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Stability Status
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Margin from Limit
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💥 What is the Chandrasekhar Limit?

The Chandrasekhar limit is the maximum mass that a white dwarf star can have while still being supported against gravitational collapse by electron degeneracy pressure. For the most common white dwarf compositions, this limit is approximately 1.44 solar masses. A white dwarf that exceeds this mass cannot exist in stable equilibrium and will either collapse into a neutron star or detonate as a Type Ia supernova.

White dwarfs are the remnants of stars like our Sun that have exhausted their nuclear fuel. Without active fusion, they are supported entirely by the quantum mechanical pressure that arises because electrons, as fermions, cannot occupy the same quantum state. This pressure is called electron degeneracy pressure, and unlike thermal pressure it does not depend on temperature. However, when the mass grows too large, relativistic effects reduce the effectiveness of this pressure and a critical threshold is reached.

The limit was derived by the Indian-American astrophysicist Subrahmanyan Chandrasekhar in 1930, when he was just 19 years old and traveling by ship from India to England. He combined special relativity with the Fermi-Dirac statistics of electrons to show that a degenerate star above about 1.4 solar masses could not be stable. The result was controversial at first, but was later confirmed and earned Chandrasekhar the 1983 Nobel Prize in Physics.

The Chandrasekhar limit is fundamental to two major areas of modern astrophysics. In stellar evolution, it marks the boundary between white dwarf stability and catastrophic collapse. In cosmology, it underpins the use of Type Ia supernovae as standard candles for measuring cosmic distances, which led to the 1998 discovery of the accelerating expansion of the universe. This calculator lets you compute the limit for any composition and check whether a given white dwarf mass is safely below it.

📐 Formula

MCh  =  5.83 ÷ μe2  ×  M☉
MCh = Chandrasekhar limit mass (solar masses)
5.83 = dimensionless constant derived from relativistic quantum mechanics
μe = mean molecular weight per electron (A/Z for fully ionized matter)
M☉ = one solar mass (1.989 × 1030 kg)
Example: For a C/O white dwarf with μe = 2.0: MCh = 5.83 / 4.0 = 1.4575 M☉

The constant 5.83 comes from integrating the Lane-Emden equation for a relativistic polytrope with index n = 3, combined with the ratio of fundamental constants (ℏ c / G)3/2. The formula shows that the limit scales as 1/μe2: compositions with a higher mass-to-electron ratio produce a lower limit.

📖 How to Use This Calculator

Steps

1
Choose a mode. Use Compute Limit to find the Chandrasekhar mass for any composition. Use Check Stability to test whether a specific white dwarf mass is below the limit.
2
Set the mean molecular weight per electron. Enter a value for μe or drag the slider. For helium, carbon, or oxygen white dwarfs use 2.0. For iron-peak compositions use approximately 2.15.
3
Read the result. In Compute Limit mode the calculator shows the Chandrasekhar mass in solar masses and kilograms. In Check Stability mode it shows the limit, the stability status, and how far the white dwarf sits from the threshold.

💡 Example Calculations

Example 1 — Standard Carbon-Oxygen White Dwarf

Carbon-oxygen white dwarf with μe = 2.0

1
For fully ionized carbon (A=12, Z=6) and oxygen (A=16, Z=8), both give μe = A/Z = 2.0.
2
Apply the formula: MCh = 5.83 / (2.0)2 = 5.83 / 4.0 = 1.4575 M☉.
3
Convert to kilograms: 1.4575 × 1.989 × 1030 = 2.899 × 1030 kg.
Chandrasekhar Limit = 1.4575 M☉ (2.899 × 1030 kg)
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Example 2 — Iron-Peak Composition

Iron-peak white dwarf core with μe = 2.15

1
For iron-56 (A=56, Z=26), μe = 56/26 = 2.154. Using 2.15 as a round value for iron-peak material.
2
Apply the formula: MCh = 5.83 / (2.15)2 = 5.83 / 4.6225 = 1.2612 M☉.
3
Convert to kilograms: 1.2612 × 1.989 × 1030 = 2.509 × 1030 kg.
Chandrasekhar Limit = 1.2612 M☉ (2.509 × 1030 kg)
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Example 3 — Checking Stability of a Near-Limit White Dwarf

White dwarf mass 1.37 M☉ with C/O composition (μe = 2.0)

1
Chandrasekhar limit for μe = 2.0 is 1.4575 M☉ (from Example 1).
2
Compare: 1.37 M☉ is below 1.4575 M☉. Margin = 1.4575 − 1.37 = 0.0875 M☉.
3
A white dwarf this close to the limit would only need to accrete about 0.09 M☉ more to trigger a Type Ia supernova, comparable to the mass of a small rocky planet accreted over millions of years.
Status = Stable, 0.0875 M☉ below the limit
Try this example →

❓ Frequently Asked Questions

What is the Chandrasekhar limit in solar masses?+
The Chandrasekhar limit is approximately 1.44 solar masses for a carbon-oxygen white dwarf. Using the formula M_Ch = 5.83 / mue^2 with mue = 2.0 gives 1.4575 solar masses. The commonly cited value of 1.4 or 1.44 is a rounded approximation of this result.
What happens when a white dwarf exceeds the Chandrasekhar limit?+
When a white dwarf exceeds the Chandrasekhar limit, electron degeneracy pressure can no longer support it. The outcome depends on the accretion rate and composition. In most cases in binary systems, the white dwarf detonates as a Type Ia supernova. In isolated cases, it may collapse to a neutron star. Either way, the white dwarf is destroyed in a fraction of a second.
Why does composition affect the Chandrasekhar limit?+
Composition sets the mean molecular weight per electron (mue), which determines how many electrons are available per unit mass to provide degeneracy pressure. For helium, carbon, and oxygen the ratio A/Z equals 2, giving mue = 2.0. For iron, A/Z = 56/26 = 2.15, so there are fewer electrons per unit mass and the limit is lower at about 1.26 solar masses.
Who discovered the Chandrasekhar limit?+
Subrahmanyan Chandrasekhar derived the limit in 1930 at age 19 during a voyage from India to England. He published the relativistic treatment in 1931 and 1935. Sir Arthur Eddington famously rejected the result at first, delaying wider acceptance by years. Chandrasekhar shared the 1983 Nobel Prize in Physics for this work and related contributions.
Is the Chandrasekhar limit exactly 1.44 solar masses?+
No. The 1.44 solar mass figure is a rounded approximation. The formula 5.83 / mue^2 with mue = 2.0 gives 1.4575 solar masses. Rapid rotation can shift the limit up to about 2.0 to 2.8 solar masses. Magnetic fields introduce smaller corrections. The exact limit also depends on which equation of state is used for the dense matter inside the white dwarf.
What are super-Chandrasekhar white dwarfs?+
Super-Chandrasekhar white dwarfs are proposed objects with masses from 2.0 to 2.8 solar masses, inferred from over-luminous Type Ia supernovae such as SN 2003fg. Rapid differential rotation or very strong magnetic fields are proposed mechanisms. They are not in stable equilibrium in the classical sense but may persist for short periods before exploding.
What is the difference between the Chandrasekhar limit and the TOV limit?+
Both are maximum mass limits for stellar remnants. The Chandrasekhar limit (about 1.4 solar masses) applies to white dwarfs and is set by the failure of electron degeneracy pressure. The Tolman-Oppenheimer-Volkoff (TOV) limit (about 2 to 3 solar masses) applies to neutron stars and is set by the failure of neutron degeneracy pressure. A white dwarf that exceeds its limit may become a neutron star, which in turn is bounded by the TOV limit.
How are Type Ia supernovae used to measure the universe?+
Because white dwarfs detonate at almost the same mass (near the Chandrasekhar limit), Type Ia supernovae have nearly uniform intrinsic peak luminosity. By comparing that known luminosity to the observed apparent brightness, astronomers can calculate the distance to the host galaxy. This technique allowed the 1998 discovery that the expansion of the universe is accelerating, evidence for dark energy.
Can the Chandrasekhar limit be derived from first principles?+
Yes. The derivation combines the relativistic kinetic energy of electrons with the Lane-Emden equation for a polytropic fluid (n = 3 for the ultra-relativistic case). The result is that there is a unique mass at which the effective polytropic index transitions through the stability boundary (gamma = 4/3), producing the formula M_Ch = 5.83 / mue^2 solar masses.
What is the most massive white dwarf ever observed?+
The heaviest confirmed white dwarfs are found in binary systems and can approach 1.3 to 1.35 solar masses. ZTF J190132.9+145808.7, discovered in 2021, has a mass of about 1.3 solar masses and extremely rapid rotation. Isolated white dwarfs rarely exceed 1.2 to 1.3 solar masses because those above about 1.0 solar masses evolve from the most massive AGB progenitors.
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What is the Chandrasekhar limit in solar masses?

The Chandrasekhar limit is approximately 1.4 solar masses for a carbon-oxygen white dwarf with a mean molecular weight per electron of 2.0. The precise value from the formula M_Ch = 5.83 / mue^2 is 1.4575 solar masses, close to the commonly quoted 1.44.

What happens when a white dwarf exceeds the Chandrasekhar limit?

When a white dwarf exceeds the Chandrasekhar limit, electron degeneracy pressure can no longer counteract gravity. The star either collapses into a neutron star or, more commonly in binary systems, triggers a Type Ia supernova. Type Ia supernovae are used as standard candles to measure cosmic distances.

Why does the Chandrasekhar limit depend on composition?

The limit depends on the mean molecular weight per electron (mue), which is the average number of atomic mass units per electron. For helium, carbon, and oxygen, mue is 2 because these nuclei have equal numbers of protons and neutrons. For iron-peak elements, the neutron-to-proton ratio is slightly higher, raising mue and lowering the limit.

Who derived the Chandrasekhar limit and when?

Subrahmanyan Chandrasekhar derived the limit in 1930 at age 19 during a ship voyage from India to England. He published the full relativistic treatment in 1931 and 1935. The discovery earned him a share of the 1983 Nobel Prize in Physics.

Is the Chandrasekhar limit exactly 1.44 solar masses?

The 1.44 solar mass figure is a rounded approximation. The exact value depends on the equation of state and the white dwarf composition. For mue = 2.0, the formula 5.83 / mue^2 gives 1.4575 solar masses. Corrections for rotation and magnetic fields can shift the limit slightly.

Can a white dwarf be more massive than the Chandrasekhar limit?

In theory, rapid rotation or strong magnetic fields can allow super-Chandrasekhar white dwarfs with masses up to about 2.0 to 2.8 solar masses. These exotic objects are inferred from some over-luminous Type Ia supernovae, but they are not in stable equilibrium the way normal white dwarfs are.

What is the mean molecular weight per electron?

The mean molecular weight per electron (mue) is the average mass per electron in units of the proton mass. For fully ionized matter it equals A / Z, where A is the mass number and Z is the atomic number. For helium (A=4, Z=2), carbon (A=12, Z=6), and oxygen (A=16, Z=8), mue = 2. For iron (A=56, Z=26), mue = 56/26 = 2.15.

What is a Type Ia supernova and how does it relate to the Chandrasekhar limit?

A Type Ia supernova occurs when a white dwarf in a binary system accretes enough mass to approach or exceed the Chandrasekhar limit. The runaway carbon fusion ignites and destroys the entire star. Because the trigger mass is nearly constant, Type Ia supernovae have nearly uniform peak luminosity, making them reliable cosmological distance indicators.

Do neutron stars have an equivalent to the Chandrasekhar limit?

Yes. The Tolman-Oppenheimer-Volkoff (TOV) limit plays the same role for neutron stars that the Chandrasekhar limit plays for white dwarfs. Above the TOV limit, neutron degeneracy pressure fails and the star collapses into a black hole. The TOV limit is estimated between 2 and 3 solar masses depending on the nuclear equation of state.

What is the formula for the Chandrasekhar limit?

The formula is M_Ch = 5.83 / mue^2 solar masses, derived from relativistic quantum mechanics. The constant 5.83 comes from the ratio (hbar c / G)^(3/2) times a dimensionless factor of order unity from integrating the Lane-Emden polytrope solution for index n = 3.

📌 Quick Tips

💡For a standard carbon-oxygen white dwarf set the mean molecular weight per electron to 2.0, which gives the classic 1.44 solar mass limit.
💡Iron-peak compositions have a higher mean molecular weight per electron (around 2.15) and therefore a lower Chandrasekhar limit, making them easier to push into collapse.
💡A white dwarf accreting matter from a binary companion approaches the limit gradually. When it crosses the limit it triggers a Type Ia supernova, not a quiet implosion.
💡The stability check mode lets you input a known white dwarf mass from a catalog and see how close it sits to the critical limit.
💡Hydrogen white dwarfs are theoretical; in practice all observed white dwarfs are helium, carbon-oxygen, or oxygen-neon-magnesium and share a mean molecular weight per electron near 2.0.