Gear Ratio, Torque & Speed Calculator
Understand Your Gear Train
For machine designers sizing a motor-to-load gear train, this calculator provides a quick way to analyze the relationship between gear tooth counts, input speed, and input torque. It’s crucial to understand how a gear pair translates power: the same tooth pair affects speed and torque in opposite ways. This tool simplifies that calculation, showing how gear ratio (GR = Nout/Nin) works with inverse speed and direct torque relations.
Use this calculator to determine the output speed and torque for any given input, helping you match motors to loads efficiently. The calculator explicitly uses GR = Nout/Nin with inverse speed and direct torque relations to ensure accurate preliminary estimations.
Gear Train Analyzer
GR = ?:? : 1
? RPM
? Nm
Formulae used:
GR = Driven ÷ Driver
Output Speed = Input Speed ÷ GR
Output Torque = Input Torque × GR
Results are approximate — verify against the governing standard or a qualified professional. This calculator is for preliminary estimation only, not a substitute for review by a qualified engineer.
How to Use This Calculator
- Enter the driver gear tooth count (must be an integer ≥ 1).
- Enter the driven gear tooth count (must be an integer ≥ 1).
- Enter the input speed in RPM.
- Enter the input torque in Nm.
- Read the gear ratio, output speed, and output torque cards, which update as you type.
FAQ
Q: How do you calculate gear ratio from tooth counts?
A: Divide the driven tooth count by the driver tooth count — GR = Nout/Nin — so 12 driver teeth and 36 driven teeth give a 3:1 ratio.
Q: Does a gear ratio multiply torque or speed?
A: It does both in opposite directions: output speed = input speed ÷ GR and output torque = input torque × GR, so a 3:1 reduction cuts speed to a third and triples torque.
Q: What does a 1:1 gear ratio mean for torque and speed?
A: With equal tooth counts GR = 1, so output speed equals input speed and output torque equals input torque — the pair only reverses rotation direction, not these values.
Q: What happens if the driver gear has zero teeth?
A: The ratio Nout/Nin is undefined, so the result cannot be calculated — the calculator blocks the output and asks for a driver tooth count of at least 1.