T
Enter valid tooth count ≥ 1.
The driving (input) gear — connected to motor/crank
T
Enter valid tooth count ≥ 1.
The driven (output) gear — connected to load
RPM
Enter to also calculate output RPM and speed
💡 GR = T₂ / T₁
GR > 1 = reduction (more torque, less speed)
GR < 1 = overdrive (less torque, more speed)
GR > 1 = reduction (more torque, less speed)
GR < 1 = overdrive (less torque, more speed)
:1
Enter a valid gear ratio > 0.
Output/Input ratio (e.g. 3 for 3:1 reduction)
RPM
Enter a valid input RPM.
💡 Output RPM = Input RPM ÷ Gear Ratio
:1
Enter a valid gear ratio.
Nm
Enter a valid torque value.
%
Typical gear pair efficiency: 95–98% (default 97%)
💡 Output Torque = Input Torque × Gear Ratio × Efficiency
⚙️ Enter up to 4 gear stages. Total ratio = GR₁ × GR₂ × GR₃ × GR₄. Leave unused stages blank.
T
Enter ≥ 1.
T
Enter ≥ 1.
T
T
T
T
RPM
Enter to calculate final output RPM
Gear Ratio
—
Sources & Methodology
Gear ratio formulas verified against Shigley’s Mechanical Engineering Design and standard gear theory references.
Machine Design — Understanding Gear Ratios
Reference for gear ratio calculation, torque multiplication, gear train analysis, and practical engineering applications in mechanical design.
Engineering Toolbox — Gear Ratio
Practical gear ratio formulae, efficiency values for different gear types, and worked examples for single-stage and multi-stage gear systems.
Gear Ratio: GR = T_driven / T_driver = input RPM / output RPM
Output RPM: N_out = N_in / GR
Output Torque: T_out = T_in × GR × (η/100) where η = efficiency %
Gear Train: GR_total = GR₁ × GR₂ × GR₃ (product of all stages)
Mechanical Advantage: MA = GR (ideal) = T_out/T_in
Efficiency 97% used as default for spur/helical gear pairs; worm gears: 50–90%
Output RPM: N_out = N_in / GR
Output Torque: T_out = T_in × GR × (η/100) where η = efficiency %
Gear Train: GR_total = GR₁ × GR₂ × GR₃ (product of all stages)
Mechanical Advantage: MA = GR (ideal) = T_out/T_in
Efficiency 97% used as default for spur/helical gear pairs; worm gears: 50–90%
⏱ Last reviewed: April 2026
How to Calculate Gear Ratio in 2026
Gear ratio (GR) is the fundamental parameter describing how a gear pair or gear train transforms rotational speed and torque. It equals the number of teeth on the driven (output) gear divided by the number of teeth on the driver (input) gear. A gear ratio greater than 1 is a reduction — speed decreases and torque increases. Less than 1 is an overdrive — speed increases and torque decreases. Power is conserved (minus friction).
The Gear Ratio Formulas
GR = T₂ / T₁ = N_in / N_out
T₂ = driven gear teeth T₁ = driver gear teeth
N_in = input RPM N_out = output RPM
Output RPM: N_out = N_in / GR
Output Torque: T_out = T_in × GR × η (where η = efficiency, 0 to 1)
Example: Driver = 20 teeth, Driven = 60 teeth, Input = 1800 RPM, Torque = 10 Nm:
GR = 60/20 = 3:1 Output RPM = 1800/3 = 600 RPM Output Torque = 10 × 3 × 0.97 = 29.1 Nm
N_in = input RPM N_out = output RPM
Output RPM: N_out = N_in / GR
Output Torque: T_out = T_in × GR × η (where η = efficiency, 0 to 1)
Example: Driver = 20 teeth, Driven = 60 teeth, Input = 1800 RPM, Torque = 10 Nm:
GR = 60/20 = 3:1 Output RPM = 1800/3 = 600 RPM Output Torque = 10 × 3 × 0.97 = 29.1 Nm
Gear Ratio Reference Table
| Gear Ratio | Speed Change | Torque Change | Typical Application |
|---|---|---|---|
| 0.5:1 | 2× speed | 0.5× torque | Overdrive gear, fan drive |
| 1:1 | No change | No change | Direction change, speed transfer |
| 2:1 | 0.5× speed | 2× torque | Light reduction, conveyor drives |
| 5:1 | 0.2× speed | 5× torque | Motor gearboxes, servo drives |
| 10:1 | 0.1× speed | 10× torque | Winches, robotic joints |
| 50:1 | 0.02× speed | 50× torque | Worm gearboxes, actuators |
| 100:1+ | Very slow | Very high | Multi-stage planetary gearboxes |
Gear Train — Multi-Stage Calculation
When multiple gear stages are connected in series, the total ratio is the product of each individual stage ratio. A three-stage gearbox with 3:1, 4:1, and 2:1 stages gives a total ratio of 3 × 4 × 2 = 24:1. This allows compact designs to achieve very high overall ratios that would be impractical with a single gear pair.
💡 Idler gears: An idler gear placed between driver and driven changes the direction of rotation but does NOT affect the gear ratio if it has a different number of teeth on its input and output (standard idler). In a compound gear train, intermediate gears DO affect the ratio if they are on the same shaft as another gear.
Frequently Asked Questions
Gear ratio is the ratio of the number of teeth on the driven (output) gear to the number of teeth on the driver (input) gear: GR = T_driven / T_driver. It equals the ratio of input RPM to output RPM. A 3:1 gear ratio means the input shaft turns 3 times for every 1 revolution of the output shaft.
GR = driven gear teeth / driver gear teeth. For a 20-tooth driver and 60-tooth driven gear: GR = 60/20 = 3:1. Alternatively, GR = input RPM / output RPM. You can also calculate it from pitch circle diameters if tooth counts are unknown: GR = PCD_driven / PCD_driver.
Output speed = input speed / GR. Output torque = input torque x GR x efficiency. For a 4:1 reduction with 1200 RPM input and 20 Nm input torque at 97% efficiency: output = 300 RPM and 77.6 Nm. Power is conserved (minus losses): P_out = P_in x efficiency.
Gear reduction: GR greater than 1 — driven gear has more teeth than driver. Output is slower but more torque. Used in gearboxes, winches, robot joints. Overdrive: GR less than 1 — driven gear has fewer teeth. Output is faster but less torque. Used in highway driving gears, bicycle cassettes, high-speed spindles.
Multiply all individual stage ratios together. Stage 1 = 3:1, Stage 2 = 4:1, Stage 3 = 2:1: total = 3 x 4 x 2 = 24:1. This compound approach allows high ratios in compact packages. Each stage can be a separate gear pair sharing a common shaft (compound gear train).
In automotive transmissions, gear ratio relates engine RPM to output shaft RPM. 1st gear has a high ratio (e.g., 3.54:1) for strong acceleration from rest. Higher gears have progressively lower ratios. Overdrive gears (e.g., 6th at 0.75:1) let the engine run slower at highway speed for fuel efficiency.
Mechanical advantage MA = output torque / input torque = gear ratio x efficiency. For a 5:1 gear at 97% efficiency: MA = 5 x 0.97 = 4.85. You apply 10 Nm and get 48.5 Nm out. Velocity ratio is the inverse: output speed = input speed / MA (ideal).
GR = input RPM / output RPM. If a motor runs at 1800 RPM and the output shaft at 600 RPM: GR = 1800/600 = 3:1. Conversely, output RPM = input RPM / GR. Knowing GR = 4:1 and input = 1200 RPM: output = 300 RPM.
Bicycle gear ratio = front chainring teeth / rear sprocket teeth. A 50-tooth chainring with 25-tooth sprocket gives GR = 2:1 — two rear wheel revolutions per pedal stroke. Development (distance per pedal stroke) = GR x wheel circumference. Smaller sprocket = higher ratio = faster but harder to pedal.
Spur gears: 96-99% per stage. Helical gears: 96-99%. Bevel gears: 95-98%. Worm gears: 50-90% (very low at high ratios due to sliding contact). For a multi-stage gearbox, total efficiency = product of all stage efficiencies. Three stages at 97% each give total efficiency of 0.97³ = 91.3%.
A simple idler gear (with the same mesh on entry and exit) reverses rotation direction but does not change the gear ratio. Only the driver and final driven gear determine the overall ratio. However, in a compound gear train where an intermediate gear is on the same shaft as another gear, it does affect the total ratio.
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