LIGO Sensitivity Band Matcher

Find which gravitational wave detector, if any, can observe a given source frequency or compact binary system.

🎯 LIGO Sensitivity Band Matcher
GW Frequency fGW (Hz)
Hz
Component Mass m₁ (M☉)
M☉
Component Mass m₂ (M☉)
M☉
Orbital Separation a (km)
km
Detector Band
—
GW Frequency
—
Matching Detector(s)
—
Sensitivity
—
Orbital Period
—

🎯 What is a LIGO Sensitivity Band Matcher?

A LIGO Sensitivity Band Matcher takes a gravitational wave frequency, either entered directly or derived from a compact binary's masses and orbital separation, and identifies which gravitational wave observatory, if any, is capable of detecting it. Gravitational wave detectors are fundamentally frequency-limited instruments: LIGO, Virgo, and KAGRA are ground-based laser interferometers tuned to roughly 10 Hz to 5,000 Hz, the planned space-based LISA mission targets the millihertz band, and pulsar timing arrays probe nanohertz frequencies from supermassive black hole binaries. A source at the wrong frequency is invisible to a given instrument no matter how strong its strain amplitude.

This calculator is useful for three common tasks: checking whether a hypothetical merger event falls inside LIGO's observing band before estimating detectability, understanding why certain astrophysical sources (like supermassive black hole binaries) require entirely different detection strategies than others (like stellar-mass black hole mergers), and building intuition for how a binary's gravitational wave frequency sweeps upward as its orbit decays, moving it through multiple detector bands over vastly different timescales.

The From Binary Masses mode applies Kepler's third law to a circular orbit: the orbital period depends only on the total mass and separation, and the gravitational wave frequency is exactly twice the orbital frequency for the dominant quadrupole radiation mode. The calculator also checks the separation against the innermost stable circular orbit (ISCO) for the given total mass; separations smaller than the ISCO correspond to a binary that has already merged, so no valid pre-merger frequency exists.

A common misconception is that "stronger" gravitational waves are always easier to detect. In reality, detectability depends on both strain amplitude and frequency: a source radiating at nanohertz frequencies, however strong, produces no signal at all in LIGO's data because the detector's noise floor rises to essentially infinite values outside its designed operating band. Frequency band matching is therefore the first filter applied before any detailed sensitivity or signal-to-noise calculation.

📐 Formula

fGW  =  2forb  =  (1/π) √(G(m1+m2)/a³)
fGW = gravitational wave frequency (Hz), twice the orbital frequency
m1, m2 = component masses (kg or M☉)
a = orbital separation (m)
G = 6.674 × 10−11 m³ kg−1 s−2
ISCO check: rISCO = 6G(m1+m2)/c²; separation must exceed rISCO
Detector bands (approximate, Hz)
PTA: 10−9 to 10−6 Hz — NANOGrav, EPTA, PPTA
LISA: 10−4 to 1 Hz — planned space-based mission
LIGO/Virgo/KAGRA: 10 to 5,000 Hz — peak sensitivity 20 to 300 Hz

📖 How to Use This Calculator

Steps

1
Select mode - Choose From Frequency to classify a known gravitational wave frequency directly, or From Binary Masses to derive the frequency from component masses and orbital separation.
2
Enter parameters - For frequency mode, type the GW frequency in Hz. For binary mode, enter both component masses in solar masses and the orbital separation in km.
3
Click Calculate - Press Calculate to see the matching detector band, which observatories cover it, and a qualitative sensitivity rating.

💡 Example Calculations

Example 1 - LIGO Peak Sensitivity Frequency

Direct frequency input: f = 150 Hz

1
150 Hz falls between 20 and 300 Hz, the "bucket" of the Advanced LIGO noise curve
2
This is the band where strain sensitivity reaches its best value, roughly 3 × 10−24 per root-Hz
Band = LIGO/Virgo/KAGRA - Peak Sensitivity | Detectors = LIGO, Virgo, KAGRA
Try this example →

Example 2 - GW150914-like Binary Black Hole Inspiral

Binary masses: m₁ = 36 M☉, m₂ = 29 M☉, a = 1,000 km

1
Total mass M = 65 M☉; ISCO separation rISCO = 6GM/c² ≈ 576 km, well below the 1,000 km input
2
Orbital period T = 2π√(a³/GM) ≈ 67.64 ms → forb ≈ 14.78 Hz → fGW = 2forb ≈ 29.57 Hz
Orbital Period ≈ 67.64 ms | fGW ≈ 29.57 Hz | Band = LIGO/Virgo/KAGRA - Peak Sensitivity
Try this example →

Example 3 - Supermassive Black Hole Binary (PTA Source)

Binary masses: m₁ = m₂ = 109 M☉, a = 0.01 pc ≈ 3.086 × 1011 km

1
Total mass M = 2 × 109 M☉, far too large for LIGO to ever probe at any realistic separation
2
Orbital period T ≈ 2.09 years → fGW ≈ 3.03 × 10−8 Hz, squarely in the nanohertz pulsar timing array band
fGW ≈ 3.03 × 10−8 Hz | Band = Pulsar Timing Array (PTA) Band | Detectors = NANOGrav, EPTA, PPTA, IPTA
Try this example →

Example 4 - LISA-Band Massive Black Hole Binary

Binary masses: m₁ = m₂ = 105 M☉, a = 3,000,000 km

1
Total mass M = 2 × 105 M☉, typical of an intermediate/massive black hole binary years before merger
2
fGW ≈ 9.98 × 10−3 Hz, inside the millihertz LISA band, well below LIGO's 10 Hz floor
fGW ≈ 9.98 × 10−3 Hz | Band = LISA Band (Space-Based)
Try this example →

❓ Frequently Asked Questions

What frequency range can LIGO actually detect?+
Advanced LIGO is sensitive from about 10 Hz to 5,000 Hz, with peak strain sensitivity (about 3 x 10^-24 per root-Hz) between roughly 20 and 300 Hz. Below 10 Hz seismic noise dominates; above a few kHz quantum shot noise dominates.
Why can't LIGO detect supermassive black hole mergers?+
Supermassive black hole binaries (10^6 to 10^9 solar masses) merge at gravitational wave frequencies of nanohertz to microhertz, ten to twelve orders of magnitude below LIGO's 10 Hz floor. Their long orbital periods, months to years, place them squarely in the pulsar timing array band instead.
What is a pulsar timing array?+
A pulsar timing array (PTA) uses the extremely regular pulses of millisecond pulsars scattered across the galaxy as a galaxy-scale gravitational wave detector. Passing nanohertz gravitational waves from supermassive black hole binaries create tiny, correlated timing deviations across the pulsar array. NANOGrav, EPTA, PPTA, and IPTA collaborations reported evidence for a stochastic gravitational wave background in 2023.
What is LISA and what band does it cover?+
LISA (Laser Interferometer Space Antenna) is a planned space-based detector using three spacecraft in a 2.5 million km triangular formation, targeting the millihertz band (about 0.1 mHz to 1 Hz). This band captures massive black hole mergers, extreme mass-ratio inspirals, and the early inspiral of stellar-mass binaries years before they chirp into LIGO's band.
How is gravitational wave frequency related to orbital frequency?+
For the dominant quadrupole radiation mode, gravitational wave frequency is exactly twice the orbital frequency: f_GW = 2 f_orb. This is because the mass quadrupole of an orbiting binary repeats its orientation twice per orbit.
What does this calculator's ISCO check mean?+
The innermost stable circular orbit (ISCO) at r = 6GM/c^2 marks the last stable circular orbit before rapid infall and merger. If you enter a separation smaller than the ISCO for the given total mass, the calculator flags an error because the binary would already have merged, so there is no valid GW frequency to classify.
Why is there a gap between LISA and LIGO?+
The 1 to 10 Hz decihertz band has no operating detector today. Ground-based interferometers cannot reach it because of seismic noise, and space-based LISA is not designed to reach it either. Proposed missions like DECIGO and the Big Bang Observer aim to fill this gap in the coming decades.
Do Virgo and KAGRA cover the same band as LIGO?+
Yes. Virgo (Italy) and KAGRA (Japan) are both ground-based laser interferometers with a similar overall design and comparable frequency coverage to LIGO, roughly 10 Hz to a few kHz. Operating multiple detectors together improves sky localization and helps distinguish real signals from instrumental noise.
What is an example of a source that crosses detector bands?+
A binary black hole system spends millions of years slowly inspiraling through the LISA millihertz band, then, in its final minutes to seconds, sweeps up through the decihertz gap and chirps through LIGO's 10 to 5,000 Hz band before merging. Multi-band observation of the same source by LISA and LIGO years apart is a key science goal of next-generation gravitational wave astronomy.
Why does the calculator show an orbital period in binary mass mode?+
The orbital period is the direct output of Kepler's third law for the given masses and separation. Halving it gives the orbital frequency, and doubling that gives the gravitational wave frequency, since GW emission occurs at twice the orbital frequency for a circular binary.
Tags: Ligo Sensitivity Band Gravitational Wave Detector Band Ligo Frequency Range LISA Band Calculator Pulsar Timing Array Frequency Gravitational Wave Detector Matcher Calculator Formula Free Online

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What frequency range can LIGO actually detect?

Advanced LIGO is sensitive from about 10 Hz to 5,000 Hz, with peak strain sensitivity (about 3 x 10^-24 per root-Hz) between roughly 20 and 300 Hz. Below 10 Hz seismic noise dominates; above a few kHz quantum shot noise dominates.

Why can't LIGO detect supermassive black hole mergers?

Supermassive black hole binaries (10^6 to 10^9 solar masses) merge at gravitational wave frequencies of nanohertz to microhertz, ten to twelve orders of magnitude below LIGO's 10 Hz floor. Their long orbital periods, months to years, place them squarely in the pulsar timing array band instead.

What is a pulsar timing array?

A pulsar timing array (PTA) uses the extremely regular pulses of millisecond pulsars scattered across the galaxy as a galaxy-scale gravitational wave detector. Passing nanohertz gravitational waves from supermassive black hole binaries create tiny, correlated timing deviations across the pulsar array. NANOGrav, EPTA, PPTA, and IPTA collaborations reported evidence for a stochastic gravitational wave background in 2023.

What is LISA and what band does it cover?

LISA (Laser Interferometer Space Antenna) is a planned space-based detector using three spacecraft in a 2.5 million km triangular formation, targeting the millihertz band (about 0.1 mHz to 1 Hz). This band captures massive black hole mergers, extreme mass-ratio inspirals, and the early inspiral of stellar-mass binaries years before they chirp into LIGO's band.

How is gravitational wave frequency related to orbital frequency?

For the dominant quadrupole radiation mode, gravitational wave frequency is exactly twice the orbital frequency: f_GW = 2 f_orb. This is because the mass quadrupole of an orbiting binary repeats its orientation twice per orbit.

What does this calculator's ISCO check mean?

The innermost stable circular orbit (ISCO) at r = 6GM/c^2 marks the last stable circular orbit before rapid infall and merger. If you enter a separation smaller than the ISCO for the given total mass, the calculator flags an error because the binary would already have merged, so there is no valid GW frequency to classify.

Why is there a gap between LISA and LIGO?

The 1 to 10 Hz decihertz band has no operating detector today. Ground-based interferometers cannot reach it because of seismic noise, and space-based LISA is not designed to reach it either. Proposed missions like DECIGO and the Big Bang Observer aim to fill this gap in the coming decades.

Do Virgo and KAGRA cover the same band as LIGO?

Yes. Virgo (Italy) and KAGRA (Japan) are both ground-based laser interferometers with a similar overall design and comparable frequency coverage to LIGO, roughly 10 Hz to a few kHz. Operating multiple detectors together improves sky localization and helps distinguish real signals from instrumental noise.

What is an example of a source that crosses detector bands?

A binary black hole system spends millions of years slowly inspiraling through the LISA millihertz band, then, in its final minutes to seconds, sweeps up through the decihertz gap and chirps through LIGO's 10 to 5,000 Hz band before merging. Multi-band observation of the same source by LISA and LIGO years apart is a key science goal of next-generation gravitational wave astronomy.

Why does the calculator show an orbital period in binary mass mode?

The orbital period is the direct output of Kepler's third law for the given masses and separation. Halving it gives the orbital frequency, and doubling that gives the gravitational wave frequency, since GW emission occurs at twice the orbital frequency for a circular binary.

📌 Quick Tips

💡LIGO's sweet spot is roughly 20 to 300 Hz, right where stellar-mass black hole and neutron star mergers cross during the final seconds before coalescence.
💡Below about 10 Hz, ground-based detectors lose sensitivity to seismic noise and Newtonian gravity-gradient noise, no matter how well isolated the mirrors are.
💡Supermassive black hole binaries (millions to billions of solar masses) emit at nanohertz frequencies, far too low for LIGO. They are the target of pulsar timing arrays instead.
💡LISA, a planned space-based detector, targets the millihertz band, filling the gap between pulsar timing arrays and ground-based interferometers.
💡A binary's GW frequency rises as it inspirals (separation shrinks), so a single system can sweep through multiple detector bands over its lifetime, just at very different timescales.