Gearbox Output Speed Calculator

Technical article

Understand Gearbox Output Speed Calculator

This calculator finds a gearbox's output speed n₂ from input speed n₁ and gear ratio i, or solves for either of the other two quantities. It shows how the standardized speeds of electric motors are matched to an application's actual required output speed through a gearbox.

What does this quantity describe?

For a gear pair with ratio i, output speed is inversely proportional to the ratio: n₂ = n₁/i. A reduction (i > 1) lowers speed, while a step-up ratio (i < 1) raises it.

A typical 4-pole electric motor on a 50 Hz supply has a synchronous speed of n_sync = 120·f/pole count = 120·50/4 = 1,500 rpm, in practice somewhat lower due to slip. If an application needs to run at only 600 rpm, a gearbox with the matching reduction ratio is placed between motor and application.

Formula and variables

n₂ = n₁ / i

n₂ = n₁ / i
n₁ = n₂ · i
i = n₁ / n₂

Symbol / input	Meaning
Output speed n₂	The speed of the driven (output) gear. As a result it follows from n₁/i.
Input speed n₁	The speed of the driving gear in revolutions per minute. Source: a tachometer or the drive motor's nameplate.
Gear ratio i	The gear ratio i = n₁/n₂ = z₂/z₁. Source: computed from the tooth counts (see the ratio calculator) or the gearbox nameplate.

Choose the inputs correctly

Enter two of the three quantities. Output speed requires input speed and ratio, input speed requires output speed and ratio, ratio requires both speeds. Use the real motor speed under load for n₁ where possible, not the theoretical synchronous speed.

How to use the calculator

Select the target quantity and enter the two known values with units. If you only know the motor type, first find synchronous speed via n_sync = 120·f/pole count, then subtract the manufacturer-stated slip for the real speed.

Worked example

Given n₁ = 1,500 rpm and i = 2.5, substitution gives n₂ = 1,500/2.5 = 600 rpm.

Understand the result and units

An output speed of 600 rpm shows the actual speed of the driven shaft for this motor and ratio. For sizing downstream components such as pulleys, conveyor belts or mixers, this output speed is the key input value.

Rotational speeds are given in revolutions per minute (rpm). Gear ratio i is a dimensionless ratio.

Typical applications

The calculation is used for gearbox selection in conveying systems, mixers, pumps, fans and machine tool spindles, matching a required application speed to a standardized motor speed.

Assumptions, limits and common mistakes

The formula assumes ideal, slip-free gear transmission. Real gearboxes with backlash or belt drives with slip give an actual output speed slightly different from n₂; for induction motors, the input speed n₁ itself already deviates from the theoretical synchronous speed.

Common mistake: Do not use synchronous motor speed (e.g. 1,500 rpm for a 4-pole 50 Hz motor) uncritically as the actual operating speed — induction motors typically run 2-6% slower than synchronous due to slip. Also, for multi-stage gearboxes, do not confuse a single stage's ratio with the overall ratio.

Frequently asked questions

Why does an electric motor often spin at 1,500 rpm?

Because a 4-pole motor on a 50 Hz supply has a synchronous speed of n_sync = 120·50/4 = 1,500 rpm. Real induction motors run somewhat slower due to slip.

What is the difference between synchronous and actual motor speed?

Synchronous speed follows directly from line frequency and pole count. Induction motors need slip to generate torque and so run 2-6% slower than synchronous in reality.

How do I find the ratio needed for a desired output speed?

Rearrange the formula as i = n₁/n₂. For 1,500 rpm input and a desired 600 rpm output, i = 2.5.