OneCalcApp LogoOneCalcAppConvert. Calculate. Simplify.

Gear Ratio Calculator

EngineeringInstant resultsFormula shown100% in your browser

Calculate gear ratio, output speed and torque for a gear pair or a gearbox.

Inputs

How to use this calculator: Gear Ratio Calculator

Calculate gear ratio, output speed and torque for a gear pair or a gearbox. The example below is calculated by this page's real engine from the displayed inputs.

  1. 1Confirm that the Gear Ratio Calculator matches the quantity or design check you need.
  2. 2Enter Driver gear teeth, Driven gear teeth, and Input speed using the units printed beside each field.
  3. 3Check every value before calculating, especially decimal points and measurement units.
  4. 4Calculate, then follow the substituted equations in the worked example and compare the result with any stated limit.
  5. 5Read the assumptions, warnings and cited references before using the result for a financial, medical or engineering decision.

Input guide and example values

Use values from the same measurement basis and time period. Conditional fields appear only when the related option is selected.

InputExample valueWhy it matters
Driver gear teeth20Measured or known driver gear teeth used by the calculation engine.
Driven gear teeth60Measured or known driven gear teeth used by the calculation engine.
Input speed1440 RPMMeasured or known input speed used by the calculation engine.
Input torque10 NmOptional input; leave the supplied default only when it matches your case.

Formula inputs & variables for Gear Ratio Calculator

These are the named quantities used by this calculator. When the source formula does not define a mathematical symbol, OneCalcApp keeps the real input label instead of inventing one.

Variable / inputUnitMeaning in this calculation
Driver gear teeth—Measured or known driver gear teeth used by the calculation engine.
Driven gear teeth—Measured or known driven gear teeth used by the calculation engine.
Input speedRPMMeasured or known input speed used by the calculation engine.
Input torqueNmOptional input; leave the supplied default only when it matches your case.

How the Gear Ratio Calculator works

The Gear Ratio Calculator uses Driver gear teeth, Driven gear teeth, Input speed, and Input torque to calculate Gear ratio, Output speed, Output torque, Power transmitted, and Teeth in mesh ratio. Its engine applies Ratio = driven teeth ÷ driver teeth; the worked values below come from that same live calculation rather than a separately typed example.

With Driver gear teeth 20, Driven gear teeth 60, Input speed 1440 RPM, and Input torque 10 Nm, the main worked-example result is Gear ratio = 3 : 1.

How each Gear Ratio Calculator input is used

Driver gear teeth

The Gear Ratio Calculator worked example uses Driver gear teeth = 20. This value is passed directly into the calculation, with an allowed minimum 1.

Driven gear teeth

The Gear Ratio Calculator worked example uses Driven gear teeth = 60. This value is passed directly into the calculation, with an allowed minimum 1.

Input speed

The Gear Ratio Calculator worked example uses Input speed = 1440 RPM. This value is passed directly into the calculation, with an allowed minimum 0.

Input torque

The Gear Ratio Calculator worked example uses Input torque = 10 Nm. This value is passed directly into the calculation, with an allowed minimum 0.

Gear Ratio Calculator formulas and result interpretation

Formula 1: relationship used

In the Gear Ratio Calculator, Ratio = driven teeth ÷ driver teeth. The quantities in this relationship come from the named inputs or from an earlier calculation step shown in the worked example.

Formula 2: relationship used

In the Gear Ratio Calculator, Output RPM = input ÷ ratio. The quantities in this relationship come from the named inputs or from an earlier calculation step shown in the worked example.

Formula 3: relationship used

In the Gear Ratio Calculator, Output torque = input torque × ratio × efficiency. The quantities in this relationship come from the named inputs or from an earlier calculation step shown in the worked example.

Gear ratio

For the displayed Gear Ratio Calculator worked example, Gear ratio is 3 : 1. speed reduction Verify Driver gear teeth, Driven gear teeth, and Input speed and their units before relying on this output.

Output speed

For the displayed Gear Ratio Calculator worked example, Output speed is 480 RPM. Verify Driver gear teeth, Driven gear teeth, and Input speed and their units before relying on this output.

Output torque

For the displayed Gear Ratio Calculator worked example, Output torque is 29.1 Nm. 97% efficiency Verify Driver gear teeth, Driven gear teeth, and Input speed and their units before relying on this output.

Power transmitted

For the displayed Gear Ratio Calculator worked example, Power transmitted is 1.508 kW. Verify Driver gear teeth, Driven gear teeth, and Input speed and their units before relying on this output.

Teeth in mesh ratio

For the displayed Gear Ratio Calculator worked example, Teeth in mesh ratio is 20 : 60. Verify Driver gear teeth, Driven gear teeth, and Input speed and their units before relying on this output.

Gear Ratio Calculator accuracy, checks and limitations

  • Gear Ratio Calculator units check: confirm Driver gear teeth, Driven gear teeth, Input speed (RPM), and Input torque (Nm) before calculating.
  • Gear Ratio Calculator result check: compare Gear ratio, Output speed, Output torque, Power transmitted, and Teeth in mesh ratio with the substituted formula steps and the displayed rounding precision.
  • Gear Ratio Calculator: Use this result for preliminary design and cross-checking. Confirm the applicable code edition, manufacturer data, site conditions and qualified-engineer approval before final design or installation.

Formula, derivation and worked example

Gear ratio is the tooth count of the driven gear divided by the driver. A ratio above 1 reduces speed and multiplies torque; below 1 it does the opposite. Real gearboxes lose a little in friction, so 97% efficiency per stage is assumed here.

Ratio = driven teeth ÷ driver teeth
Output RPM = input ÷ ratio
Output torque = input torque × ratio × efficiency

Substitution steps

  1. 1. Ratio
    driven ÷ driver teeth
    = 3
  2. 2. Output speed
    input ÷ ratio
    = 480 RPM

Computed example results

Gear ratio
3 : 1
speed reduction
Output speed
480 RPM
Output torque
29.1 Nm
97% efficiency
Power transmitted
1.508 kW
Teeth in mesh ratio
20 : 60

Understanding the result

Read the main result together with supporting checks, assumptions, limits and intermediate values.

For a manual check, repeat the first equation, confirm the units and change one input at a time.

Assumptions and calculation scope

  • Input speed is assumed to be entered in RPM; converting from another unit before entry avoids changing the numerical meaning of the calculation.
  • Gear Ratio Calculator applies the displayed Ratio = driven teeth ÷ driver teeth relationship to the entered engineering inputs. Factors that are not exposed as inputs or stated assumptions are outside this calculator's calculation scope.

Common mistakes when using Gear Ratio Calculator

  • Do not mix units for Input speed (RPM), Input torque (Nm). A unit mismatch changes the input magnitude even when the typed number looks reasonable.
  • Do not replace the displayed Ratio = driven teeth ÷ driver teeth relationship with a different convention without also changing the underlying assumptions; compare like-for-like methods when checking the result.
  • Do not treat Gear ratio = 3 : 1 from the worked example as a universal answer. It belongs to the displayed example inputs and must be recalculated for the actual case.

When the Gear Ratio Calculator is useful

Gear Ratio Calculator is designed for cases where Driver gear teeth, Driven gear teeth, Input speed, Input torque are known and you need Gear ratio, Output speed, Output torque. The page keeps the live calculator, calculation method and worked example together so the result can be checked instead of treated as a black-box number.

Use the calculator for the scope described by its inputs and notes. The displayed method is Ratio = driven teeth ÷ driver teeth. If the real project or decision needs factors that are not represented here, treat the result as an estimate and add the missing checks separately.

Driver gear teeth and Driven gear teeth: what changes the answer

The worked example uses Driver gear teeth = 20, Driven gear teeth = 60, Input speed = 1440 RPM, Input torque = 10 Nm. With those values, Gear ratio is 3 : 1. Changing an input should be interpreted according to that field's unit, range, option and hint rather than by the number alone.

For this calculator, the main input roles are: Driver gear teeth: Measured or known driver gear teeth used by the calculation engine. Driven gear teeth: Measured or known driven gear teeth used by the calculation engine. Input speed (RPM): Measured or known input speed used by the calculation engine. Input torque (Nm): Optional input; leave the supplied default only when it matches your case.

How to sanity-check a Gear Ratio Calculator result

Start by confirming the entered values and units, then compare the substituted working with the displayed formula or calculation steps. Pay particular attention to Gear ratio, because it is the first worked-example output shown by the live engine.

Finally, compare the result with the assumptions, warnings and related calculators on this page. A nearby calculator can be useful as a cross-check when it measures the same workflow from a different input or output direction.

Next logical calculator

Continue with Pulley Size & RPM Calculator

Pulley Size & RPM Calculator is directly connected from Gear Ratio Calculator as a source-defined continuation or comparison.

Open Pulley Size & RPM Calculator

Formula

  • Ratio = driven teeth ÷ driver teeth
  • Output RPM = input ÷ ratio
  • Output torque = input torque × ratio × efficiency

Gear ratio is the tooth count of the driven gear divided by the driver. A ratio above 1 reduces speed and multiplies torque; below 1 it does the opposite. Real gearboxes lose a little in friction, so 97% efficiency per stage is assumed here.

Worked example

  1. 120-tooth driver and 60-tooth driven → ratio 3:1.
  2. 21,440 RPM in gives 480 RPM out.
  3. 310 Nm in gives about 29 Nm out after losses.

Tips

  • Keep the tooth counts non-integer multiples (e.g. 21:60) so the same teeth do not always mesh — it wears more evenly.
  • Multi-stage gearboxes multiply their ratios: 3:1 then 4:1 gives 12:1.

Frequently asked questions

What does a 3:1 gear ratio mean?

The input turns three times for every one turn of the output, giving three times the torque.

Can I use diameters instead of teeth?

Yes — for meshing gears the pitch diameters give the same ratio.

Does gearing change power?

No, only the balance of speed and torque. Power out equals power in minus friction losses.

What inputs does the Gear Ratio Calculator use?

It uses Driver gear teeth, Driven gear teeth, Input speed, and Input torque. Follow the unit printed for each field and choose any selectable option to match the real scenario.

What does the Gear Ratio Calculator calculate?

It calculates Gear ratio, Output speed, Output torque, Power transmitted, and Teeth in mesh ratio. With the displayed default inputs, Gear ratio is 3 : 1.

Which formula does the Gear Ratio Calculator use?

The primary relationship is Ratio = driven teeth ÷ driver teeth. The page also shows substituted values and calculation steps so the result can be checked independently.

How can I verify a Gear Ratio Calculator result?

First verify the units for Driver gear teeth, Driven gear teeth, and Input speed. Then compare the substituted formula steps with Gear ratio and its displayed precision.

What are the limitations of the Gear Ratio Calculator?

Gear Ratio Calculator: Use this result for preliminary design and cross-checking. Confirm the applicable code edition, manufacturer data, site conditions and qualified-engineer approval before final design or installation.

Related calculators

Keep going with more engineering tools.

Pulley Size & RPM Calculator

Find the driven pulley speed or the pulley size needed to reach a target RPM.

Motor RPM Calculator

Find an AC motor's speed from its number of poles and supply frequency, including slip.

Belt Length Calculator

Find the belt length needed between two pulleys from their diameters and centre distance.

Pressure Calculator & Converter

Convert between bar, psi, kPa and metres of water head — and see the pressure at the bottom of a tank.

Air Flow & Compressor CFM Calculator

Size an air compressor from tool demand and duty cycle, convert CFM to L/min or m³/h, and check tank runtime between PSI limits.

Water Pump HP Calculator

Find the pump horsepower needed to lift water to your tank from the flow rate, total height and pipe losses.

Related Engineering Articles

Deeper reading on the engineering behind this calculation.

How to Calculate Percentage Increase, Decrease & Change

Learn how to calculate percentage increase, decrease, change, and difference with simple formulas, step-by-step examples, and practical calculations.

Read Article →

Dilution Ratios Explained: How to Calculate 1:10 to 1:1000 Mixes

What 1:N really means, how to convert any dilution ratio into ounces per gallon or ml per litre, worked examples from 1:10 to 1:1000, and a printable ratio chart.

Read Article →