Gear Ratio Calculator
Calculate gear ratios, RPM, speed, and torque for simple and compound gear trains. Perfect for automotive, bicycle, mechanical engineering, and robotics applications. Enter gear teeth counts or diameters to find output RPM, speed, and torque.
What Is a Gear Ratio?
A gear ratio is the ratio of the number of teeth on the driven gear (output) to the number of teeth on the drive gear (input). It determines the relationship between input and output speed, torque, and mechanical advantage.
The key formulas used in gear calculations are:
Gear Ratio (GR) = Number of Teeth on Driven Gear ÷ Number of Teeth on Drive Gear
Output RPM = Input RPM ÷ GR
Output Torque = Input Torque × GR × Efficiency
Output Speed = (Output RPM × π × Wheel Diameter) ÷ 60
A gear ratio greater than 1 means the output shaft rotates slower than the input shaft but has more torque (speed reduction). A ratio less than 1 means the output shaft rotates faster but with less torque (overdrive). Compound gear trains multiply the ratios of each gear pair.
Understanding Gear Types
- Spur Gears: Most common, straight teeth, parallel shafts, efficient (95-98%).
- Helical Gears: Angled teeth, smoother and quieter, handles higher loads (90-95%).
- Bevel Gears: Cone-shaped, changes axis of rotation (intersecting shafts).
- Worm Gears: High reduction ratios (20:1 to 300:1), self-locking, low efficiency (50-85%).
❓ Gear Ratio Calculator FAQ
What is a gear ratio?
A gear ratio is the ratio of the number of teeth on the driven gear to the number of teeth on the drive gear. It determines how speed and torque are transformed between input and output shafts.
How do I calculate gear ratio?
Gear Ratio = Number of Teeth on Driven Gear ÷ Number of Teeth on Drive Gear. For example, if the drive gear has 20 teeth and the driven gear has 60 teeth, the gear ratio is 60 ÷ 20 = 3:1.
What does a gear ratio of 3:1 mean?
A 3:1 gear ratio means the driven gear has 3 times more teeth than the drive gear. The output shaft rotates 3 times slower than the input shaft, but produces 3 times more torque (assuming 100% efficiency).
What is the difference between underdrive and overdrive?
Underdrive (GR > 1) reduces speed and increases torque. Overdrive (GR < 1) increases speed and reduces torque. Overdrive is commonly used in vehicles for highway cruising to reduce engine RPM.
How do I calculate output RPM from gear ratio?
Output RPM = Input RPM ÷ Gear Ratio. For example, if input RPM is 1000 and gear ratio is 3:1, output RPM = 1000 ÷ 3 = 333.33 RPM.
How do I calculate output torque from gear ratio?
Output Torque = Input Torque × Gear Ratio × Efficiency. For example, 50 N·m × 3 × 0.95 = 142.5 N·m.
What is a compound gear train?
A compound gear train uses multiple gear pairs where the driven gear of one pair is connected to the drive gear of the next pair on the same shaft. The total gear ratio is the product of the ratios of each pair.
How do I calculate the total ratio of a compound gear train?
Total Gear Ratio = GR₁ × GR₂ × GR₃ × ... where each GR is the ratio of a gear pair. For example, 2:1 × 3:1 = 6:1 total ratio.
What is the difference between spur and helical gears?
Spur gears have straight teeth and are efficient (95-98%) but can be noisy. Helical gears have angled teeth, run smoother and quieter, can handle higher loads, but have slightly lower efficiency (90-95%).
What is the efficiency of a gear train?
Efficiency is the ratio of output power to input power. Typical efficiencies: spur gears 95-98%, helical 90-95%, bevel 90-95%, worm 50-85%. This calculator includes efficiency in torque calculations.
How do I calculate vehicle speed from gear ratio?
Vehicle Speed = (Output RPM × π × Wheel Diameter) ÷ 60. This gives speed in units per minute (e.g., meters per minute). Convert to km/h or mph by multiplying by 60 and converting units.
What is the difference between a drive gear and a driven gear?
The drive gear (or input gear) is connected to the power source. The driven gear (or output gear) is connected to the load. The gear ratio is driven ÷ drive.
What is an idler gear?
An idler gear is a gear placed between two other gears to change the direction of rotation or to bridge a distance. It does not affect the overall gear ratio.
How do I calculate the number of teeth needed for a desired gear ratio?
If you know the desired ratio and the number of teeth on one gear, you can calculate the other: Driven Teeth = Drive Teeth × Gear Ratio. For example, to get a 3:1 ratio with a 20-tooth drive gear, you need 20 × 3 = 60 teeth on the driven gear.
What is the center distance between two gears?
The center distance is the distance between the centers of two meshing gears. It depends on the pitch diameters of the gears. This calculator does not compute center distance, but it's important for gear design.
What is the difference between pitch diameter and outside diameter?
Pitch diameter is the diameter where the gear teeth mesh. Outside diameter is the total diameter including the teeth. This calculator uses teeth count to determine the gear ratio.
Can I use this calculator for bicycle gear ratios?
Yes. For bicycles, the drive gear is the front chainring and the driven gear is the rear cog. Enter the number of teeth on each. The output speed will be the bicycle's speed based on wheel diameter.
How do I calculate gear reduction for a motor?
If you have a motor with a known RPM and torque, and you need a specific output RPM and torque, use the gear ratio formulas. This calculator helps you find the right ratio for your application.
What is the difference between gear ratio and gear reduction?
Gear ratio is the general term for the ratio of teeth between gears. Gear reduction specifically refers to a gear ratio greater than 1 that reduces speed and increases torque.