How do I calculate gear ratio?

Divide the driven gear's tooth count by the driver's. A 12-tooth driver into a 36-tooth gear is 36/12 = 3, written 3:1. Output speed is input speed divided by the ratio, and output torque is input torque multiplied by it.

Does a gearbox increase power?

No. It trades speed for torque, and the product — power — is unchanged apart from losses. A reduction gear gives more torque at lower speed; the power output is always slightly less than the input because of friction in the mesh and bearings.

What is the difference between a gear ratio and a gear train?

A gear ratio describes one pair of gears. A gear train is several pairs in series, and the overall ratio is the product of the individual ratios. Idler gears in a train change the direction and the spacing but not the overall ratio.

How do I work out compound gear ratios?

Multiply the individual stage ratios. A 3:1 stage followed by a 4:1 stage gives 12:1 overall. Compound trains are used when a single pair would need an impractically large gear — the same ratio is achieved in a much smaller envelope.

What efficiency should I assume?

About 98–99% per mesh for spur gears, 95–98% for helical, and lower for worm drives — a single-start worm can be under 50%. Add bearing losses of about 1% per shaft. A multi-stage gearbox's overall efficiency is the product of the stage efficiencies.

Gear Ratio Calculator

Speed ratio, output speed and torque multiplication for a two-gear drive from the tooth counts and input speed.

Data verified 2026-09-29 · based on n/a — standard engineering relationships, no single governing revision

Quick Answer

Gear ratio is N_driven ÷ N_driver. A 12-tooth driver into a 36-tooth gear gives a 3:1 reduction — output speed is one third and output torque three times the input (ignoring losses). Power is unchanged.

Gear Ratio and Output

Driver teeth

Driven teeth

Input speed (RPM)

Input torque (lb·in)

The Formulas Used

Gear ratio: i = n₂ ÷ n₁ (driven teeth ÷ driver teeth)
Output speed: n_out = n_in ÷ i
Output torque: T_out = T_in × i × η where η is the drive efficiency

Torque Multiplies, Power Does Not

A gear pair trades speed for torque. Whatever the ratio, the power through the drive is unchanged — that is the conservation of energy. A 3:1 reduction gives three times the torque at one third the speed, and the product is the same.

That is why a gearbox cannot create capacity, only reshape it. If a motor is too small for a load, gearing it down will let it move a heavier load slower, but it cannot make the job go faster. And because every stage has losses — typically 1 to 3% per mesh for spur gears — a multi-stage box delivers slightly less power out than in, never more.

Frequently Asked Questions

How do I calculate gear ratio?: Divide the driven gear's tooth count by the driver's. A 12-tooth driver into a 36-tooth gear is 36/12 = 3, written 3:1. Output speed is input speed divided by the ratio, and output torque is input torque multiplied by it.
Does a gearbox increase power?: No. It trades speed for torque, and the product — power — is unchanged apart from losses. A reduction gear gives more torque at lower speed; the power output is always slightly less than the input because of friction in the mesh and bearings.
What is the difference between a gear ratio and a gear train?: A gear ratio describes one pair of gears. A gear train is several pairs in series, and the overall ratio is the product of the individual ratios. Idler gears in a train change the direction and the spacing but not the overall ratio.
How do I work out compound gear ratios?: Multiply the individual stage ratios. A 3:1 stage followed by a 4:1 stage gives 12:1 overall. Compound trains are used when a single pair would need an impractically large gear — the same ratio is achieved in a much smaller envelope.
What efficiency should I assume?: About 98–99% per mesh for spur gears, 95–98% for helical, and lower for worm drives — a single-start worm can be under 50%. Add bearing losses of about 1% per shaft. A multi-stage gearbox's overall efficiency is the product of the stage efficiencies.

Value Sources

Each data column on this page is tied to the source it came from. The numbers in square brackets correspond to the table headers above.

#	Source	Type	Revision / method
[1]	ASME B1.1 — Unified Inch Screw Threads	standard	ASME B1.1-2019 — source
[2]	ASTM A615 — Deformed steel bars for concrete reinforcement	standard	ASTM A615/A615M-20 — source
[3]	ASTM E140 — Hardness Conversion Tables	standard	ASTM E140-12b — source
[4]	Values computed in your browser	derived	Evaluated locally from the formulas shown on the page. No data leaves the device.
[5]	ISO 4287 — Surface texture: Profile method	standard	ISO 4287:1997 — source
[6]	ISO 68-1 — Basic profile	standard	ISO 68-1:2023 — source
[7]	NFPA 70 NEC Table 310.16	standard	NEC 2023 (NFPA 70-2023) — source

Data Sources

Standard	Revision	What it covers on this page
Formulas as shown on this page	n/a — standard engineering relationships, no single governing revision	every value this calculator produces

Cross-checked against:

Formulas verified against the corresponding reference chart on this site, so the calculator and the published tables agree

Derived values — the following values on this page are calculated, not taken directly from the standard:

Value	How it is derived
All outputs	Computed in the browser from the formulas above. No data leaves the device.

Outputs are computed from the formulas shown. Verify against the governing standard for design or acceptance work.

Accuracy and use. The values on this page are compiled from the published standards and cross-checked sources listed above. Where values are derived, the derivation is stated. No warranty, express or implied, is made as to the accuracy or completeness of this information, and no liability is accepted for any loss or damage arising from its use. Engineering reference data is provided for guidance in preliminary work — before a value is used for design, fabrication or acceptance testing, verify it against the current revision of the governing standard and against your own inspection. The user assumes all risk and responsibility in connection with the use of this information.

Cite This Page

Every value on this page is traceable to the sources listed above. If you use the data in a document, paper or report, cite it as:

Plain text

Engineering Reference. "Gear Ratio Calculator." https://refmanual.com/calculators/gear-ratio/ (accessed 2026-09-29). Data from Formulas as shown on this page, n/a — standard engineering relationships, no single governing revision.

BibTeX

@misc{gear-ratio,
  title        = {Gear Ratio Calculator},
  author       = {{Engineering Reference}},
  howpublished = {\url{https://refmanual.com/calculators/gear-ratio/}},
  note         = {Accessed: 2026-09-29},
  source       = {Formulas as shown on this page, n/a — standard engineering relationships, no single governing revision}
}

RIS (EndNote, Zotero, Mendeley)

TY  - ELEC
TI  - Gear Ratio Calculator
AU  - Engineering Reference
PB  - Engineering Reference
UR  - https://refmanual.com/calculators/gear-ratio/
PY  - 2026
DA  - 2026-09-29
N1  - Source: Formulas as shown on this page, n/a — standard engineering relationships, no single governing revision
ER  -

Each row in the tables above also has a permanent link — hover a row and use the # link to cite a single value rather than the whole page.