# Gear Train Ratio, Output Speed and Torque Calculator

> Source: https://netray.co/tools/gear-train-ratio-output-speed-and-torque-calculator
> Publisher: Netray (netray.co), AI and integration engineering for ERP and manufacturing systems.
> Section: Free Tools

## Short answer

Enter tooth counts for a two-stage spur or helical reduction and get overall ratio, output speed, output torque and output power after mesh losses.

## Category

engineering-plm

## Industry

Industrial Machinery

## Audience

- Design engineer
- Application engineer
- Estimator

## Tool

**Kind:** calculator

**Inputs:**

#### Input power

**Key:** motor_kw

**Type:** number

**Default:** 7.5

**Min:** 0.1

**Step:** 0.1

**Unit:** kW

**Help:** Power at the input shaft of the first stage.

#### Input speed

**Key:** motor_rpm

**Type:** number

**Default:** 1750

**Min:** 1

**Step:** 10

**Unit:** rpm

**Help:** A 4-pole motor at 60 Hz runs near 1750 rpm under load.

#### Stage 1 driver teeth (pinion)

**Key:** z1

**Type:** number

**Default:** 18

**Min:** 6

**Step:** 1

**Unit:** teeth

#### Stage 1 driven teeth (gear)

**Key:** z2

**Type:** number

**Default:** 54

**Min:** 6

**Step:** 1

**Unit:** teeth

#### Stage 2 driver teeth (pinion)

**Key:** z3

**Type:** number

**Default:** 20

**Min:** 6

**Step:** 1

**Unit:** teeth

**Help:** Sits on the same shaft as the stage 1 driven gear.

#### Stage 2 driven teeth (gear)

**Key:** z4

**Type:** number

**Default:** 60

**Min:** 6

**Step:** 1

**Unit:** teeth

#### Efficiency per mesh

**Key:** eff

**Type:** number

**Default:** 98

**Min:** 85

**Max:** 100

**Step:** 0.1

**Unit:** %

**Help:** Well-made spur or helical meshes are typically 97 to 99 percent. Use a lower value for worm or poorly lubricated gears.

**Outputs:**

#### Input torque

**Key:** in_torque

**Expr:** motor_kw * 9549.3 / motor_rpm

**Format:** decimal

**Description:** T (N.m) = 9549.3 x P (kW) / n (rpm).

#### Stage 1 ratio

**Key:** ratio1

**Expr:** z2 / z1

**Format:** decimal

#### Stage 2 ratio

**Key:** ratio2

**Expr:** z4 / z3

**Format:** decimal

#### Overall reduction ratio

**Key:** total_ratio

**Expr:** ratio1 * ratio2

**Format:** decimal

**Description:** Product of the two stage ratios, input : output.

#### Output speed (rpm)

**Key:** out_rpm

**Expr:** motor_rpm / total_ratio

**Format:** decimal

**Primary:** true

#### Output power (kW)

**Key:** out_power

**Expr:** motor_kw * pow(eff / 100, 2)

**Format:** decimal

**Description:** Input power times mesh efficiency once per stage.

#### Output torque (N.m)

**Key:** out_torque

**Expr:** out_power * 9549.3 / out_rpm

**Format:** decimal

**Primary:** true

#### Torque multiplication

**Key:** torque_gain

**Expr:** out_torque / in_torque

**Format:** decimal

**Description:** Slightly less than the ratio because of mesh losses.

**Chart:**

#### Output speed vs stage 1 gear teeth

**Type:** line

**X:** z2

**From:** 20

**To:** 100

**Steps:** 40

**Series:**

- out_rpm

**Disclaimer:** Kinematic and power-balance estimate only. Gear strength (AGMA 2001 or ISO 6336), bearing loads and thermal rating must be verified separately.

## Content

**Intro:** This calculator works out the overall ratio, output speed, output torque and output power of a two-stage gear reduction from the tooth counts. It is the first check an engineer or estimator makes before sizing gears, selecting a gearmotor or quoting a custom gearbox.

**Sections:**

#### How to use the calculator

**Body:** Enter the input power and speed at the first shaft, then the tooth counts of the four gears. Stage 1 is the pinion (driver) and gear (driven) on the first pair; stage 2 is the second pair, with its pinion keyed to the same shaft as the stage 1 gear. Set the efficiency per mesh, then read the overall ratio, output rpm and output torque. The chart sweeps the stage 1 gear tooth count so you can see how output speed moves when you change the ratio split.

**Bullets:**

- Tooth counts must be whole numbers
- Keep pinion tooth count above the undercut limit, typically 17 for a 20 degree pressure angle
- Use the tooth-count sweep to compare ratio options quickly

#### The formulas behind it

**Body:** Ratio of one mesh is driven teeth divided by driver teeth. For a compound train the overall ratio is the product of the stage ratios. Output speed is input speed divided by the overall ratio. Torque follows from power: T in N.m equals 9549.3 times power in kW divided by speed in rpm. Each mesh passes about 97 to 99 percent of power, so output power is input power times efficiency raised to the number of meshes. Idler gears change direction but not ratio.

#### Worked example and how to read it

**Body:** With 7.5 kW at 1750 rpm, an 18:54 first stage and a 20:60 second stage, each stage is 3:1 so the overall ratio is 9:1. Output speed is about 194 rpm. Input torque is about 40.9 N.m and, with 98 percent per mesh, output torque is about 353 N.m. If the result is far from your target speed, change one tooth count at a time. Prefer tooth combinations with no common factor between pinion and gear, which spreads wear more evenly (hunting tooth).

#### Common mistakes

**Body:** The most frequent error is treating ratio as output over input, which inverts the answer. Another is ignoring that stage 2 runs at the speed of the stage 1 gear, not the motor speed. Efficiency is also often forgotten, which overstates output torque by a few percent. Finally, a correct ratio says nothing about whether the teeth will survive the load: bending and pitting checks per AGMA 2001 or ISO 6336 are still required.

**Cta:** If you quote or configure gearboxes in an ERP, Netray can wire ratio and torque checks into the quoting and item-master workflow so engineering data is not retyped.

**Faq:**

#### How do I calculate the gear ratio of a two-stage gear train?

**Answer:** Divide the driven teeth by the driver teeth for each mesh, then multiply the two stage ratios together. For example 54/18 is 3 and 60/20 is 3, so the overall ratio is 9 to 1. Output speed equals input speed divided by that overall ratio.

#### Why is output torque less than ratio times input torque?

**Answer:** Every gear mesh loses a small share of power to sliding friction, churning and bearing drag. Typical spur and helical meshes are 97 to 99 percent efficient, so two stages lose roughly 2 to 6 percent of the power, which shows up as slightly lower torque.

#### Does an idler gear change the ratio?

**Answer:** No. An idler meshes with both the driver and the driven gear, so its tooth count cancels out of the ratio. It only reverses the direction of rotation and changes the center distance between the two shafts. It still adds one mesh of loss.

#### What is a hunting tooth ratio?

**Answer:** A hunting tooth combination uses pinion and gear tooth counts with no common factor, so each pinion tooth meets every gear tooth before a pair repeats. This evens out wear and helps spread any tooth error. Examples are 19 and 54, or 23 and 60.

## Search terms

gear ratio calculator, gear train calculator, two stage gear reduction calculator, gear output speed calculator, gear torque calculator, compound gear train ratio, gearbox ratio calculator, speed reducer torque calculation

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