Gears trade speed for torque. Enter the teeth on the driving and driven gears (or pulley diameters), the input speed and torque to get the ratio, output speed and output torque.
Enter the teeth of both gears.
Enter the input speed, torque and efficiency.
Read the output speed and torque.
Ratio: i = N_driven ÷ N_driver
Output: rpm_out = rpm_in ÷ i, T_out = T_in × i × η
Gears and belt pulleys trade speed for torque. This calculator takes the number of teeth on the driving and driven gears, or the diameters of two pulleys, along with the input speed in rpm, the input torque in N·m and the transmission efficiency. It returns the gear ratio, the output speed and the output torque after losses.
In India the question comes up constantly: matching a 1440 rpm induction motor to a flour chakki, a pump or a conveyor, choosing sprockets for a motorcycle, or understanding how a bicycle's gears make hills easier. Mechanical engineering students meet it in theory of machines, and ITI and diploma students use it in workshop practice. The same arithmetic works for gear pairs, chain and sprocket drives, and V-belt pulleys.
1. Count the teeth on the driver (input) and driven (output) gears, or measure the pitch diameters of the pulleys.
2. Compute the gear ratio i = driven ÷ driver.
3. Find the output speed: rpm_out = rpm_in ÷ i.
4. Find the ideal output torque: T_out = T_in × i.
5. Allow for losses by multiplying the torque by the efficiency η as a decimal: T_out = T_in × i × η.
6. For a gear train, multiply the ratios of each stage to get the overall ratio.
Two meshing gears must move their teeth past the contact point at the same rate, or they would slip or jam. If the driver has N₁ teeth and turns at n₁ rpm, it passes N₁n₁ teeth per minute, and the driven gear must pass the same number: N₂n₂ = N₁n₁. So n₂ = n₁ × N₁ ÷ N₂. For pulleys, the belt's surface speed is the same on both, which gives the same relation with diameters in place of teeth, ignoring belt slip, which is usually a few percent.
Mechanical power is torque times angular speed, P = 2πnT ÷ 60 with n in rpm. An ideal gear pair cannot create power, so if the output turns three times slower, it must deliver three times the torque. Real gears lose some power to friction in the teeth and bearings, so the output torque is reduced by the efficiency. Speed is unaffected by losses because it is fixed by the teeth. A good spur gear pair may be around 95 to 98% efficient.
A ratio greater than 1 is a reduction: slower and stronger, used in pumps, mills and vehicle first gears. A ratio less than 1 is an overdrive: faster and weaker, used in bicycles' top gears and in some fans and blowers. An idler gear placed between two others changes the direction of rotation but not the overall ratio, because its teeth cancel out of the calculation. Worm gears are special: a single-start worm gives a large reduction in one stage but with lower efficiency.
Gurpreet's flour chakki is driven by a 1440 rpm motor with a 100 mm pulley and a V-belt to a 400 mm pulley on the mill shaft, with 25 N·m motor torque and about 94% belt efficiency.
Gear ratio: driven ÷ driver = 400 ÷ 100 = 4 : 1
Output speed: 1440 ÷ 4 = 360 rpm
Output torque: 25 × 4 × 94% = 94 N·m
Answer: Gear ratio 4 : 1; Output speed 360 rpm; Output torque 94 N·m
Swapping driver and driven, which turns a reduction into an overdrive.
Mixing teeth on one side with diameter on the other.
Applying efficiency to the speed instead of the torque.
Adding the ratios of a multi-stage gear train instead of multiplying them.
Forgetting belt slip, which makes a pulley drive run slightly slower than calculated.
Selecting pulleys for chakkis, pumps, compressors and workshop machines.
Choosing motorcycle and bicycle sprockets for speed or climbing.
Designing gearboxes for conveyors, mixers and robotics projects.
Theory of machines coursework for mechanical engineering and ITI students.
Checking whether a motor can deliver enough torque at the output shaft.
What about a gear train?
Multiply the ratios of each stage.
Does an idler gear change the ratio?
No, it only reverses the direction.