Model compact binaries and their wave imprint. Flexible inputs cover frequency, period, or separation easily. Export results to CSV and PDF for reports fast.
This calculator uses the leading-order quadrupole inspiral approximation for the dimensionless gravitational-wave strain amplitude from a circular compact binary:
Characteristic strain is estimated as hc ≈ h·√(f·T) using your observation time T.
| m1 (M☉) | m2 (M☉) | Distance (Mpc) | f (Hz) | Pattern factor | Typical h (order) |
|---|---|---|---|---|---|
| 30 | 30 | 500 | 100 | 1.0 | ~10-22 |
| 10 | 1.4 | 100 | 150 | 0.7 | ~10-22 |
| 1.4 | 1.4 | 40 | 300 | 1.0 | ~10-21 |
These are rough orders for intuition; use the calculator for exact values.
Gravitational-wave strain h is a dimensionless measure of fractional stretching and squeezing of spacetime. A value near 10-21 means a one‑meter baseline changes by about 10-21 meters at peak response. This calculator estimates the leading-order inspiral strain from a compact binary, letting you compare scenarios quickly.
The amplitude depends most strongly on the chirp mass Mc. For component masses m1 and m2, Mc = (m1·m2)3/5 /(m1+m2)1/5. Because the formula uses Mc5/3, doubling Mc increases strain by about 25/3 ≈ 3.17.
Inspiraling binaries radiate gravitational waves at twice the orbital frequency. You can enter f directly, derive it from orbital period using f = 2/P, or estimate it from separation with Kepler’s law. Ground-based detectors often observe tens to thousands of hertz, while space-based concepts target millihertz bands.
Strain decreases as 1/d, so doubling distance halves the predicted signal. For example, a system giving h ≈ 1×10-21 at 40 Mpc would be near 2.5×10-22 at 160 Mpc, all else equal. This makes distance the fastest lever for sensitivity studies.
Real signals depend on sky location, polarization, and inclination. The pattern factor in this tool scales the strain to explore unfavorable versus favorable geometries. Values below 1 mimic average orientations, while values near 1–2 approximate near-optimal alignment with the detector response.
If you supply an observation time T, the calculator also estimates characteristic strain using hc ≈ h·√(f·T). Longer coherent observation increases hc, which is useful when comparing to detector sensitivity curves plotted in hc.
Double neutron stars (about 1.4+1.4 M☉) can reach strains around 10-21 at tens of megaparsecs near merger frequencies. Stellar-mass black hole binaries (tens of M☉) can be detectable farther away, often producing strains around 10-22 to 10-21, depending on distance, frequency, and orientation.
Start with component masses and a plausible distance, then sweep frequency to see how the amplitude changes. Next, vary pattern factor to bound best and worst cases. Finally, add observation time to estimate hc for a chosen band. Export CSV or PDF runs to document assumptions and share comparisons.
Strain h is the fractional change in length caused by a passing gravitational wave. It is dimensionless and typically extremely small, often near 10-22 to 10-21 for astrophysical sources at accessible distances.
Chirp mass combines both bodies in the way that controls inspiral amplitude and frequency evolution. In the leading-order strain formula, the amplitude scales as Mc5/3, making it the dominant mass parameter.
No. It is a leading-order quadrupole inspiral estimate for circular binaries. Accurate modeling near merger needs higher‑order post‑Newtonian terms, spins, eccentricity effects, and full numerical relativity waveforms.
Use the gravitational-wave frequency in your band of interest. For many compact binaries, f increases as they inspiral. You can input f directly, compute it from period with f = 2/P, or estimate it from separation via Kepler’s law.
It scales the strain to represent orientation and detector response. Real signals depend on sky position and inclination. Use smaller values to mimic average geometry and larger values to explore more favorable alignment cases.
Characteristic strain approximates how signal strength accumulates over observation time. This calculator uses hc ≈ h·√(f·T). It is useful for comparisons with sensitivity curves that are often plotted in terms of hc.
Yes. Compute h and optionally hc, then compare against published sensitivity curves for the relevant band and detector. Keep units consistent, note the assumed distance and orientation, and remember this is an approximation.
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.