Gear Mesh Frequency Calculator
Enter the input shaft speed and the tooth counts of each mesh to find the gear mesh frequency (GMF = teeth × shaft Hz), the gear ratio, the output speed, the 1X–3X harmonics, the expected sidebands, and the hunting tooth frequency — for single, two, or three-stage gearboxes. These are the marker frequencies you look for in a measured vibration spectrum.
ℹ The gear math here is exact for the tooth counts and speed you enter, but the tool is a calculator, not a measurement. It assumes a single constant input speed and ideal, correctly-meshed gears — verify your tooth counts and which gear drives. The sideband-to-defect mappings (tooth wear, eccentricity, broken tooth) are common diagnostic conventions, not a diagnosis: they tell you where to look in a spectrum measured with a calibrated accelerometer and analyzer.
Drive input
Gear stages
Schematic only — tooth counts are labelled on each gear; sizes are scaled, not to-scale engineering drawings.
Per-stage chain
How It Works
When two gears mesh, a tooth on the pinion strikes a tooth on the wheel once per tooth, once per revolution. So the rate at which teeth engage — the gear mesh frequency (GMF), also called the tooth mesh frequency — is simply the number of teeth times how fast that gear turns: GMF = N·f, where N is the tooth count and f is the shaft speed in hertz (f = RPM ÷ 60). Because the same teeth pass through the mesh on both gears, the GMF is identical for the driver and the driven gear: Ndriver·fdriver = Ndriven·fdriven. That identity is the heart of the calculation and is what lets you cascade stages.
The gear ratio of a mesh is Ndriven ÷ Ndriver; a ratio above 1 is a speed reduction (and multiplies torque), below 1 is a speed increase. The driven shaft turns at fin ÷ ratio. For a multi-stage gearbox the output of one stage drives the next, so the overall ratio is the product of the stage ratios and the final output speed is the input divided by that product. This tool accepts input speed in RPM and converts internally (f = RPM ÷ 60); it cascades up to three stages and reports each stage’s ratio, shaft speed, and GMF, plus the overall ratio and output RPM.
In a measured spectrum the GMF rarely stands alone. It usually appears with harmonics at 2X and 3X the mesh frequency, and it is flanked by sidebands spaced at a shaft’s rotation rate — GMF ± k·fshaft. The spacing of those sidebands is the clue: sidebands a pinion-revolution apart point at the pinion, wheel-spaced sidebands point at the wheel. This sideband pattern is a core element of gearbox vibration analysis and predictive-maintenance condition monitoring programs in wind turbines, industrial speed reducers, and automotive transmissions. Knowing the expected gearbox frequency components — the GMF, its harmonics, and the characteristic gear fault frequencies such as sideband families around harmonics — is what lets an analyst distinguish a mesh problem from a bearing or shaft fault in the same spectrum. Finally, the hunting tooth frequency (HTF = GMF·GCD(T1,T2) ÷ (T1·T2)) is the rate at which one specific pinion tooth re-meets one specific wheel tooth — relevant to wear and to the gear designer’s choice of a “hunting” tooth combination (GCD = 1).
The interpretations below are standard diagnostic conventions in rotating-machinery vibration analysis (ISO 10816 and related standards). They are reliable pointers — they tell you which frequency to inspect and what it might mean — but only a calibrated measurement, trended over time and confirmed by inspection, turns a peak into a confirmed fault. Gearbox faults detected by spectrum analysis are typically verified by oil analysis (detecting metal particles) and by visual inspection during a planned maintenance window.
| What you see in the spectrum | Conventional interpretation |
|---|---|
| GMF and 2X/3X GMF rise together | General mesh wear, tooth-profile error, or increasing load on the mesh. |
| Sidebands around GMF spaced at one gear’s 1X shaft rate | Eccentricity, misalignment, or a bent shaft on that gear; modulation of the mesh by once-per-rev geometry. |
| Growing 1X-shaft sidebands plus rising GMF harmonics | Progressing tooth wear on the gear whose shaft sets the sideband spacing. |
| Impacts / a burst once per revolution of one shaft (1X shaft rate, broadband) | A localised defect such as a cracked or broken tooth striking once per turn. |
| A raised peak at the hunting tooth frequency / its low-order multiples | Faults tied to a specific repeating tooth-pair contact; relevant when GCD > 1. |