Calculate gear ratio from tooth counts, output speed and torque, mechanical advantage, and power transfer. Supports single and compound 2-stage gear trains with efficiency loss.
The gear ratio determines how rotational speed and torque are traded between the input (driver) and output (driven) gears. A ratio greater than 1:1 is a reduction — it slows the output but multiplies torque by the same factor. A ratio less than 1:1 is an overdrive — it speeds up the output but reduces torque. The fundamental relationship is: Gear Ratio = Driven Teeth / Driver Teeth.
Gear trains are everywhere: bicycles, automobiles, industrial machinery, clocks, power tools, and robotics. Understanding gear ratios is essential for selecting the right combination of speed and torque for any mechanical application. Compound (multi-stage) gear trains multiply individual stage ratios for very high total reductions.
This calculator computes gear ratio, output speed and torque, power transfer with efficiency losses, and mechanical advantage. It supports single-stage and 2-stage compound gear trains, includes a reference table of common applications, and generates comparison tables showing how different tooth counts affect performance.
Designing gear trains requires balancing speed, torque, size, and efficiency. This calculator provides instant gear ratio analysis with power loss estimates, visual speed-torque comparison charts, and tooth-count exploration tables — replacing iterative trial-and-error with systematic comparison. Keep these notes focused on your operational context. Tie the context to the calculator’s intended domain. Use this clarification to avoid ambiguous interpretation.
Gear Ratio: GR = N_driven / N_driver (tooth count ratio) Output Speed: ω_out = ω_in / GR Output Torque: τ_out = τ_in × GR × η Power: P = τ × ω = τ × (2π × RPM / 60) Compound gear train: GR_total = GR₁ × GR₂ × ... × GRₙ η_total = η₁ × η₂ × ... × ηₙ
Result: Ratio = 0.348:1 (overdrive), Output = 230 RPM, 13.2 N·m
A bicycle with 46-tooth chainring and 16-tooth cog: GR = 16/46 = 0.348:1. This is an overdrive — the wheel spins 2.875× faster than the pedals. Input at 80 RPM and 40 N·m → Output: 230 RPM, 13.2 N·m (at 95% chain efficiency). Power: 335 W input = 318 W output.
Spur gears handle ratios from 1:1 to about 6:1 per stage efficiently. Helical gears offer smoother operation and slightly higher ratios. Bevel gears redirect rotation by 90°. Worm gears achieve 10:1 to 100:1 in a single stage but with lower efficiency (50-90%). Planetary gear sets combine sun, planet, and ring gears for compact 3:1 to 10:1 ratios in a coaxial arrangement.
Gears conserve power (minus friction losses): P_in = P_out / η. Since power = torque × angular velocity, reducing speed by a factor of N multiplies torque by N (times efficiency). This is why first gear in a car provides the most torque (highest ratio) but the lowest top speed. The total transmission ratio from engine to wheels combines the gear ratio and the final drive (differential) ratio.
Real gear train design involves more than ratio calculation: center distance must match, tooth profiles must avoid interference, materials must handle contact stress, and lubrication must control heat. Module (metric) or diametral pitch (imperial) defines tooth size. The gear ratio calculator provides the kinematic foundation; detailed mechanical design requires additional analysis of stress, noise, and thermal constraints.
Both give the same result because tooth pitch must be identical for meshing gears. The ratio of diameters equals the ratio of tooth counts. Using tooth counts is more practical because you can count teeth directly.
A compound train uses multiple stages of gear pairs on shared shafts. Each stage multiplies the ratio. Two stages of 3:1 give a 9:1 total ratio, but in a much smaller package than a single 9:1 pair (which would need very different gear sizes).
Each gear mesh loses 1-5% of power to friction between teeth, bearing friction, and lubricant churning. More stages mean more meshes and more losses. Typical efficiency: spur gears 95-98%, helical 96-99%, worm gears 30-90% depending on ratio.
For gears, they\'re numerically equal (before efficiency losses). Gear ratio = speed reduction = torque multiplication = mechanical advantage. With 97% efficiency, actual torque multiplication is 0.97× the gear ratio.
Yes — this is called overdrive or speed-up. The driven gear has fewer teeth than the driver, so it spins faster but with less torque. Bicycle high gears, wind turbine gearboxes, and automotive top gears are common examples of ratios < 1:1.
Start with the required output speed and torque, then work backward: GR = desired torque / motor torque = motor speed / desired speed. Check that both gears have reasonable tooth counts (usually 12-120 for spur gears) and that motor power exceeds output power/efficiency.