Gravitational Wave Chirp Mass Calculator

Calculate the chirp mass of a merging compact binary — the single combination of two masses that a gravitational-wave detector measures most precisely — along with total mass, mass ratio, and an ISCO merger-frequency estimate, visualized as the real upward-sweeping frequency "chirp."

Gravitational wave chirp mass calculator

The chirp mass is the one combination of a compact binary's two masses that a gravitational-wave detector like LIGO/Virgo measures most precisely — it alone sets the leading-order rate at which the signal's frequency sweeps upward as the two objects spiral together:

$M_c = \frac{(M_1 M_2)^{3/5}}{(M_1+M_2)^{1/5}}$

Also computed below: total mass $M_1+M_2$ , mass ratio $q = M_2/M_1$ , symmetric mass ratio $\eta = M_1 M_2/(M_1+M_2)^2$ , and the reduced mass $\mu = M_1 M_2/(M_1+M_2)$ .

Mass 1 (

M_1

)

Mass 2 (

M_2

)

M☉

M_c

≈ 26.117 M☉

Total mass 60 M☉ · mass ratio q = 1 · η = 0.25 · reduced mass 15 M☉

ISCO frequency estimate ≈ 73.267 Hz — an order-of-magnitude "where it ends" marker, not an exact numerical-relativity merger frequency.

The characteristic "chirp": gravitational-wave frequency rising from about 16.882 Hz toward an ISCO-frequency estimate of about 73.267 Hz as the two masses spiral together, from the leading-order post-Newtonian relation $f(t) \propto (t_c-t)^{-3/8}$ .

A stylized strain sketch built from the same frequency sweep — oscillation speeds up and grows in amplitude toward merger, the shape that gives the "chirp" its name.

Scope of this tool: the ISCO frequency estimate treats the merger as a test particle reaching the innermost stable circular orbit around a single Schwarzschild mass equal to the binary's total mass. It's a genuinely useful order-of-magnitude "where the signal roughly ends" marker, not the precise frequency a full numerical-relativity simulation would give — the true merger typically happens a little later, at a somewhat higher frequency, once strong-field two-body effects this estimate ignores take over. The frequency-sweep formula itself is the standard leading (Newtonian-quadrupole) post-Newtonian approximation, accurate for the early-to-mid inspiral but not for the final orbits immediately before merger.

When two black holes or neutron stars spiral together, the gravitational waves they radiate sweep upward in frequency right up until merger — the “chirp” that gives these signals their name. Buried in the shape of that sweep is one specific combination of the two masses that a detector like LIGO or Virgo can pin down far more precisely than either mass on its own: the chirp mass.

The formula

M_c = \frac{(M_1 M_2)^{3/5}}{(M_1+M_2)^{1/5}}

$M_1$ and $M_2$ are the two component masses. From the same pair, this calculator also reports the total mass $M_1+M_2$ , the mass ratio $q = M_2/M_1$ , and the symmetric mass ratio:

\eta = \frac{M_1 M_2}{(M_1+M_2)^2}

(which ranges from 0 for a wildly unequal pair up to a maximum of 0.25 for two equal masses), and the reduced mass $\mu = M_1 M_2/(M_1+M_2)$ .

Why chirp mass, specifically?

To leading (Newtonian-quadrupole) order, the rate at which the gravitational-wave frequency rises depends on the two masses only through $M_c$ :

f(t) = \frac{1}{\pi}\left(\frac{5}{256\,(t_c-t)}\right)^{3/8}\left(\frac{G M_c}{c^3}\right)^{-5/8}

where $t_c$ is the time of coalescence and $t$ counts down toward it. Because this sweep rate is directly observable in the data (it’s literally the shape of the signal), the chirp mass comes out of a detection with a far smaller uncertainty than the total mass or the individual masses — both of which depend on higher-order post-Newtonian terms and are consequently measured far less precisely. This is exactly why LIGO/Virgo papers always quote chirp mass first, and to many more significant figures than anything else about the source.

Two real events worth knowing

GW150914 (September 2015), the first direct detection: two black holes of roughly 36 and 29 solar masses merged, radiating a chirp mass around 28 M☉. A simplified, commonly used stand-in for the same event — two 30 M☉ black holes — reproduces a chirp mass of about 26.1 M☉, close to the same ballpark and a useful round illustrative pairing.
GW170817 (August 2017), the first (and so far only confirmed) neutron star merger seen in gravitational waves: component masses around 1.17–1.60 M☉ gave a chirp mass of 1.188 M☉ (+0.004/−0.002) — one of the most precisely measured chirp masses of any gravitational-wave event, and a striking demonstration of just how tightly this one parameter can be pinned down.

Reading the two visuals

The frequency-sweep chart plots the actual leading-order chirp — gravitational-wave frequency rising as the two masses spiral together over roughly the final second or so before merger, using the current chirp mass. The curve’s characteristic upward-curving shape, steepening dramatically in the last moments, is the real physics behind the name “chirp.” A marker shows an ISCO-frequency estimate of where the signal is expected to roughly end.
The waveform sketch below it is a stylized strain plot built from the same frequency sweep — oscillating faster and growing in amplitude toward merger, the recognizable shape from real LIGO strain plots.

An honest caveat about the merger frequency

The ”≈ merger” marker on the chart comes from the innermost stable circular orbit (ISCO) for the total mass — treating the merger, very roughly, as a test particle reaching the last stable orbit around a single Schwarzschild black hole of that mass:

f_{\rm ISCO} \approx \frac{c^3}{6^{3/2}\,\pi\, G\, M_{\rm total}}

This is a genuinely useful order-of-magnitude “where it roughly ends” marker — not a precise numerical-relativity merger frequency. Real merger simulations, which account for the strong-field two-body dynamics this estimate ignores entirely, find the true merger happens a little later and at a somewhat higher frequency than this simple ISCO estimate suggests. Likewise, the frequency-sweep formula itself is the leading post-Newtonian term — accurate through the early-to-mid inspiral, but not the final few orbits immediately before merger, where higher-order relativistic corrections start to matter.

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Changelog

2026-09-07Published.