Gear Ratio Calculator
Fast, accurate, and free online Gear Ratio Calculator tool that runs directly in your browser.
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Gear Ratio Calculator
Professional kinematic and energy analysis of drive systems with advanced diagnostics
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Calculate the gear ratio of a gear, belt or chain transmission in seconds. Enter the number of teeth or wheel diameters and find out the rotational speeds of the shafts. An ideal tool for constructors, mechanics, students and people designing machines. Accurate results, practical examples and instant calculations.
Run the gear ratio calculator See formulas and examples
What is the gear ratio
The gear ratio is the ratio of the rotational speed or the number of teeth between two mating drive elements. Determines how much the speed and torque change between the driving and driven shafts. If the first wheel rotates faster than the second, the gear is reduction; if slower – multiplicative.
Basic gear ratio formula
i = n₁ / n₂ = z₂ / z₁ = D₂ / D₁
where:
i – gear ratio
n₁ – rotational speed of the driving wheel [rpm]
n₂ – rotational speed of the driven wheel [rpm]
z₁ – number of teeth of the driving wheel
z₂ – number of teeth of the driven wheel
D₁ – diameter of the driving wheel [mm]
D₂ – diameter of the driven wheel [mm]The gear ratio is therefore a proportion that shows how many times the input shaft rotates relative to the output shaft. The valueand > 1means speed reduction (torque increase), whileand < 1- speed increase (torque reduction).
How to use the calculator
- Enter the number of teeth or wheel diameters (D₁ and D₂).
- Enter the rotational speed of the drive shaft.
- ClickCalculate- you will get the speed of the second shaft and the gear ratio.
- Additionally, you will receive information about the nature of the gear (reducing / accelerating).
Calculation examples
Reduction gear
z₁ = 20, z₂ = 60 → i = 60 / 20 = 3. n₂ = n₁ / 3. If n₁ = 1800 rpm, then n₂ = 600 rpm.
The gear reduces the speed and triples the torque.
Multiplication belt transmission
D₁ = 200 mm, D₂ = 100 mm → i = 0.5. If n₁ = 1000 rpm, then n₂ = 2000 rpm.
The gear increases the speed twice.
Chain transmission
z₁ = 18, z₂ = 36 → i = 2. n₂ = n₁ / 2. There is a speed reduction.
Two-stage transmission
Stage 1: i₁ = 3, Stage 2: i₂ = 4 → i_total = 12. This means a 12-fold increase in torque.
Speed and torque relationships
M₂ / M₁ = i
n₂ / n₁ = 1 / iAs the gear ratio increases, the speed decreases, but the torque increases. Therefore, gears are crucial in mechanisms requiring precise control of power and movement.
Types of gears
Gears
Most often used in engines, gearboxes and machine drives. Accurate, durable, but requires lubrication.
Belt transmissions
Enable quiet operation and dampen vibrations. Used in fans, machine tools and auxiliary drives.
Chain gears
Provide high durability and no slippage. Popular in bicycle and agricultural machinery drives.
Planetary gears
They enable large gear ratios with small dimensions. Used in automatic transmissions and robotics.
Frequently asked questions (FAQ)
How to calculate the gear ratio?
Divide the number of teeth or diameter of the driven gear by the driving gear. The result is the ratio.
How to calculate output speed?
n₂ = n₁ / i – the speed of the output shaft decreases with increasing gear ratio.
What does i > 1 mean?
The gear reduces speed and increases torque - typical of gearboxes and industrial gears.
Does the calculator work for multi-stage gears?
Yes, you can enter subsequent ratios, and the final result is their product.
Summary:gear ratio calculator allows you to instantly calculate the ratio of speed and torque. Perfect for mechanics, designers and technical students. Works for gear, belt and chain transmissions.