Calculate gear ratio, output RPM, and output torque from driver/driven teeth counts, using the standard gear train formulas.
Enter the teeth counts, plus input RPM and/or torque if you want output speed and torque.
Enter teeth counts and hit calculate
A gear ratio describes how two meshing gears trade speed for torque, or torque for speed, as power flows from one shaft to another. It is simply the number of teeth on the driven gear divided by the number of teeth on the driver gear. 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.
Worked example: Suppose 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 Output Torque = 5 × 3 = 15 Nm, three times stronger than the motor's own torque, 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.
It tells you how speed and torque change as power passes from one gear to the next. A ratio greater than 1 (e.g. 3:1) means the output shaft turns slower but with more torque; a ratio less than 1 means the output turns faster but with less torque.
Because power is conserved (ignoring mechanical losses), and power is the product of speed and torque. Meshing gears must move at the same linear speed at their point of contact, so a larger driven gear rotates proportionally slower than the smaller driver gear, and that lost rotational speed reappears as extra torque.
No. The gear ratio itself only needs the two teeth counts. Input RPM and input torque are optional extras — provide either or both if you also want to know the resulting output speed and output torque.
Yes — the same ratio math applies to sprocket-and-chain drives (using tooth counts) and to pulley-and-belt drives (using pulley diameters in place of teeth), since both are governed by the same principle of matching linear speed at the point of contact.
This calculator uses the ideal, loss-free gear equations taught in mechanical engineering coursework. Real gearboxes lose a small percentage of speed and torque to friction and mesh inefficiency, so for safety-critical or procurement decisions, always verify results against the manufacturer's rated efficiency and have them reviewed by a qualified engineer.