Gear Ratio & Gearbox Torque Calculator

Gear ratio formula: Gear Ratio = Driven Teeth ÷ Driver Teeth — for example, a 60-tooth driven gear and a 20-tooth driver gear gives a 3:1 ratio, tripling torque while cutting speed to one-third. A gear ratio describes how two meshing gears trade speed for torque, or torque for speed, as power flows from one shaft to another. Because the teeth on both gears must mesh at the same linear speed at the point of contact, a gear with more teeth must rotate more slowly than a gear with fewer teeth, even though both are part of the same mechanical system. This is the fundamental reason gear ratios let engineers convert a fast, low-torque input, such as a motor shaft, into a slower, high-torque output, such as a wheel axle, or the reverse.

When the driven gear has more teeth than the driver gear, the ratio is greater than 1, and the system is a reduction: output speed falls and output torque rises. When the driven gear has fewer teeth, the ratio is less than 1, and the system is an overdrive: output speed rises while torque falls. A 1:1 ratio simply passes speed and torque through unchanged. Real gearboxes, in vehicles, conveyors, winches, and robotics, are built around stacking several such ratios in series to hit a target speed and torque combination efficiently, and the same math applies whether the meshing elements are spur gears, bevel gears, or a chain-and-sprocket drive.

This calculation shows up constantly in real mechanical design work: sizing a gearbox reduction so a motor's rated RPM lands within a conveyor roller's target speed, checking whether a gear train delivers enough output torque to move a given load, or working backward from a desired output speed to pick the right pair of gears from a catalog.

Formulas Used

Example: A small motor drives a 20-tooth driver gear, which meshes with a 60-tooth driven gear connected to a conveyor roller. The motor spins at 1500 RPM and delivers 5 Nm of torque at its shaft. Gear Ratio = 60 ÷ 20 = 3, written as 3:1, meaning the driven gear turns once for every three turns of the driver gear. Output RPM = 1500 ÷ 3 = 500 RPM, and ideal Output Torque = 5 × 3 = 15 Nm — three times the motor's own torque before mechanical losses, since the gear trades the extra speed for extra rotational force. This combination of slower, more powerful rotation is exactly why reduction gearboxes are used wherever a motor needs to move a heavy load.

Compound Gear Trains: Calculating Ratio With Multiple Gears

This calculator handles one meshing pair (a single stage) at a time, but many real gearboxes stack two or more stages in series on a compound gear train — for example, four gears arranged as two meshing pairs, where the second gear on the first shaft is keyed to (rotates together with) the third gear that starts the second shaft. The overall ratio of a compound gear train is simply the product of each individual stage's ratio, not their sum: Overall Gear Ratio = Ratio (Stage 1) × Ratio (Stage 2) × … × Ratio (Stage n). To find the overall ratio for a train with several gears, calculate each meshing pair's ratio separately with this calculator, then multiply the results together.

Worked example (4 gears, 2 stages): Stage 1: a 15-tooth driver gear meshes with a 45-tooth driven gear, Ratio 1 = 45 ÷ 15 = 3. That 45-tooth gear's shaft carries a 20-tooth gear (Stage 2's driver), meshing with a 60-tooth final driven gear, Ratio 2 = 60 ÷ 20 = 3. Overall Gear Ratio = Ratio 1 × Ratio 2 = 3 × 3 = 9:1. For a motor input of 1800 RPM and 2 Nm torque: Output RPM = 1800 ÷ 9 = 200 RPM, and ideal Output Torque = 2 × 9 = 18 Nm. Notice the overall 9:1 ratio from two 3:1 stages is far more compact than trying to cut speed 9× with a single gear pair, which is exactly why compound gear trains are used to reach large reductions (or large speed increases) within a practical gearbox size.

How to Calculate Torque From Gear Ratio

Ideal output torque from a gear ratio is a direct multiplication: Output Torque = Input Torque × Gear Ratio, using the same ratio (driven teeth ÷ driver teeth, or the compound overall ratio for a multi-gear train) found above. A gear ratio greater than 1 (a reduction) always multiplies torque by that same factor while dividing speed by it; a ratio less than 1 (an overdrive) does the reverse, reducing torque while increasing speed. This ideal relationship assumes no mechanical losses — real gearboxes deliver somewhat less output torque than this formula predicts, by roughly the gearbox's rated mechanical efficiency (commonly in the 85–98% range depending on gear type and stage count), so always check the manufacturer's rated efficiency for anything beyond a preliminary estimate.

Common Mistakes When Calculating Gear Ratio

• Reversing driver and driven in the formula. The ratio is always driven teeth ÷ driver teeth. Swapping them silently flips a reduction into an overdrive and gives the wrong output speed and torque.
• Ignoring mechanical efficiency losses. This calculator uses the ideal, loss-free equations. Real gear trains lose a small percentage of speed and torque to friction and mesh inefficiency, so actual output torque will be slightly lower than the ideal figure, especially through multiple reduction stages.
• Applying a single-stage ratio to a multi-stage gearbox. A gearbox with several gear pairs in series has a combined ratio equal to the product of each individual stage's ratio, not just the first or last pair's ratio.
• Assuming diameter and teeth count are interchangeable without checking module/pitch. The ratio math is the same whether you use teeth counts or pitch diameters, but only if both gears share the same module (metric) or diametral pitch (imperial) — mismatched gears won't mesh correctly regardless of what the ratio formula returns.

Reference: The gear ratio, output speed, and output torque equations used here are standard mechanical power-transmission relationships taught in mechanical engineering coursework. This calculator is for preliminary, educational sizing only and does not replace manufacturer-rated gearbox efficiency data or a qualified engineer's review.