Gear Ratio Calculator
Calculate gear ratio, output RPM, output torque, multi-stage gear reduction, vehicle speed, or engine RPM from gear teeth, tire size, drivetrain ratios, and efficiency.
Calculator is for informational purposes only. Terms and Conditions
Choose what to solve for
Select the calculation type, drive type, and unknown value. Required inputs update automatically.
Use gear teeth for basic ratios, RPM/torque for shaft output, multi-stage for compound reductions, or vehicle mode for tire and drivetrain calculations.
The math is the same for teeth or pitch diameters, but the interpretation and rotation direction differ.
Choose the unknown value. The calculator hides the solved variable and validates only visible required inputs.
Enter the known values
Only the fields needed for the selected solve mode are shown.
Visual Check
The diagram updates to show gear reduction, overdrive, multi-stage reduction, or vehicle drivetrain relationships.
Solution
Live result, quick checks, warnings, and full solution steps.
Quick checks
- Check—
Show solution steps See the equation, conversions, substitutions, assumptions, and result path
- Enter values to see the full solution steps and checks.
Source, Standards, and Assumptions
Calculation basis, constants, assumptions, and limitations.
Source/standard information updates based on the selected calculation.
- Assumptions will appear after a valid calculation.
On this page
Calculator Guide
How to Use the Gear Ratio Calculator
The Gear Ratio Calculator above calculates gear ratio, output RPM, input RPM, output torque, input torque, multi-stage gear train ratio, vehicle speed, and engine RPM. For a simple gear pair, gear ratio is the driven gear teeth divided by the driver gear teeth. A 60-tooth driven gear and 20-tooth driver gear gives a \(3:1\) reduction.
A larger driven gear creates a reduction, which lowers output speed and increases ideal output torque. A smaller driven gear creates an overdrive, which raises output speed and lowers ideal output torque. Real systems also lose energy through gear mesh friction, bearings, chain losses, belt slip, lubrication drag, tire slip, and heat.
Quick Answer
Use \(R=N_{driven}/N_{driver}\) to calculate gear ratio from teeth. Then use \(RPM_{out}=RPM_{in}/R\) for output speed and \(T_{out}=T_{in}R\eta\) for estimated output torque with efficiency. If \(R>1\), the system is a reduction. If \(R<1\), the system is overdrive.
Gear ratio is not a full gear design check
A ratio calculation checks motion, speed, and ideal torque tradeoff. It does not check AGMA gear rating, bending stress, pitting resistance, dynamic load factor, contact ratio, pressure angle, module, diametral pitch, face width, shaft stress, bearing load, lubrication, backlash, housing stiffness, duty cycle, or thermal limits.
Gear Ratio Calculator Inputs and Outputs
The calculator uses different inputs depending on the selected solve mode. The simplest mode uses driver and driven teeth. The advanced modes add RPM, torque, efficiency, stage count, transmission ratio, axle ratio, and tire diameter.
| Type | Value | What It Means | Common Unit |
|---|---|---|---|
| Input | Driver teeth | The input gear, sprocket, or pulley member being powered. | teeth for gears/sprockets; pitch or effective diameter for pulleys |
| Input | Driven teeth | The output gear, sprocket, or pulley member being turned. | teeth for gears/sprockets; pitch or effective diameter for pulleys |
| Input | Stage count | The number of active gear stages in a compound gear train. | 1, 2, or 3 stages in this calculator |
| Input | Input RPM | Rotational speed entering the gear pair or gear train. | rpm |
| Input | Input torque | Torque applied to the driver shaft before the gear ratio is applied. | N·m, lb-ft, lb-in |
| Input | Efficiency | Estimated gear train or drivetrain efficiency used for torque calculations. | % |
| Input | Transmission ratio, axle ratio, tire diameter | Vehicle gearing values used to estimate vehicle speed or engine RPM. | ratio, inches, mph, km/h |
| Output | Gear ratio | The ratio of driven member size to driver member size. | :1 |
| Output | Output RPM and torque | The calculated speed and estimated torque after the ratio and efficiency are applied. | rpm and selected torque unit |
Gear Ratio Formula
The main gear ratio formula compares the driven member to the driver member. For gears and sprockets, use tooth counts. For belt drives, use pitch diameter or effective pulley diameter instead of outside diameter whenever accurate belt speed or ratio matters.
Main Gear Ratio Formula
\(R\) is the gear ratio. \(N_{driven}\) is the driven tooth count, and \(N_{driver}\) is the driver tooth count.
Solve for Driven or Driver Teeth
These formulas are useful for target ratios. If the answer is a decimal, round to a practical whole tooth count and recalculate the actual ratio.
Output RPM Formula
A higher reduction ratio lowers output speed. For example, a \(3:1\) reduction turns 3000 rpm input into 1000 rpm output.
Output Torque Formula
\(\eta\) is total efficiency as a decimal. A 95% efficient gear train uses \(\eta=0.95\). This is a torque estimate, not a strength rating.
Multi-Stage Gear Train Formulas
If efficiency is known per stage, total efficiency can be estimated as \(\eta_{total}=\eta_1\eta_2\eta_3\cdots\eta_n\).
Vehicle Speed and Engine RPM Formulas
These common vehicle gearing formulas use speed \(v\) in mph, tire diameter \(D\) in inches, transmission ratio \(G_t\), axle ratio \(G_a\), and engine speed in rpm.
Tire Diameter From Tire Size
This estimates nominal tire diameter in inches when tire width is in millimeters and aspect ratio is entered as a decimal, such as \(0.70\) for a 70-series tire.
What the Gear Ratio Variables Mean
Every variable describes geometry, speed, torque, efficiency, or vehicle drivetrain setup. Correctly identifying the driver and driven member is the most important step.
| Symbol | Meaning | How to Enter It |
|---|---|---|
| \(R\) | Gear ratio for one gear pair, sprocket pair, or pulley pair. | Calculated as driven divided by driver. |
| \(R_{total}\) | Total ratio of a multi-stage gear train. | Multiply each active stage ratio. |
| \(R_1, R_2, R_3\) | Individual stage ratios in a compound gear train. | Each stage is driven teeth divided by driver teeth. |
| \(N_{driver}\) | Number of teeth on the input member. | Enter a positive whole number for gears and sprockets. |
| \(N_{driven}\) | Number of teeth on the output member. | Enter a positive whole number for gears and sprockets. |
| \(RPM_{in}\) | Rotational speed entering the gear pair or gear train. | Enter in revolutions per minute. |
| \(RPM_{out}\) | Rotational speed leaving the gear pair or gear train. | Calculated from input rpm divided by ratio. |
| \(T_{in}\) | Input torque before the ratio is applied. | Enter in N·m, lb-ft, or lb-in. |
| \(T_{out}\) | Estimated output torque after ratio and efficiency. | Calculated in the selected torque unit. |
| \(\eta\) | Total efficiency factor. | Enter as a percent in the calculator; use decimal form in formulas. |
| \(G_t\) | Transmission gear ratio. | Use the selected transmission gear, such as \(0.70\), \(1.00\), or \(2.50\). |
| \(G_a\) | Axle or differential ratio. | Use the axle ratio, such as \(3.73\), \(4.10\), or \(4.56\). |
| \(D\) | Vehicle tire diameter. | Use inches when using the 336 vehicle speed constant. |
| \(v\) | Vehicle speed. | Use mph with the 336 constant or convert units first. |
How to Use the Gear Ratio Calculator
Start by selecting the solve mode that matches your known values. Then enter tooth counts, rpm, torque, efficiency, or vehicle data as needed.
Choose the calculation mode
Select gear teeth ratio, RPM and torque, multi-stage gear train, or vehicle speed/RPM depending on the problem.
Identify the driver and driven member
The driver is the input gear. The driven member is the output gear. Reversing these values changes a reduction into an overdrive.
Enter the known values and units
Use whole tooth counts for gears and sprockets. For torque, select N·m, lb-ft, or lb-in. For vehicle speed, check tire diameter units.
Round tooth-count results when needed
If solving for driver or driven teeth gives a decimal, round to a practical whole tooth count and recalculate the actual ratio.
Check the interpretation
Review whether the result is a reduction, direct drive, or overdrive. Then compare output speed, torque multiplier, and warnings.
How to Interpret Gear Ratio Results
A gear ratio tells you how many input rotations are needed for one output rotation when the ratio is written as a reduction. It also tells you the ideal speed and torque tradeoff.
| Result | Meaning | What to Check Next |
|---|---|---|
| \(R>1\) | Reduction. Output speed decreases and ideal output torque increases. | Check tooth strength, gear size, efficiency, shaft load, and required output speed. |
| \(R=1\) | Direct drive. Ideal output speed and torque are unchanged. | Check rotation direction and mechanical layout. |
| \(R<1\) | Overdrive. Output speed increases and ideal output torque decreases. | Check whether the driven equipment can handle the higher rpm. |
| Output RPM too low | The reduction ratio may be too high for the desired speed. | Use a smaller ratio or split the design into a different drivetrain layout. |
| Output torque too high | The ratio may overload downstream components even if the math is correct. | Check shafts, keys, couplings, bearings, mounts, gearbox housing, and driven equipment. |
| Fractional tooth count | The rearranged math found a target, but real gears need whole-number teeth. | Round to a practical tooth count and recalculate the actual ratio. |
What to do with the result
Use the ratio to check whether the output speed and torque match the application. For machinery and robotics, compare output rpm and torque with the load requirement. For vehicles, compare engine rpm, road speed, tire diameter, transmission ratio, and axle ratio as one complete drivetrain.
Quick sanity check
If a 20-tooth driver turns a 60-tooth driven gear, the ratio should be \(60/20=3:1\). The output should be one-third the input rpm, not three times faster. If your result moves in the wrong direction, the driver and driven values are probably reversed.
Input Quality Checklist
Gear ratio calculations are simple, but the wrong input convention can produce a result that looks correct while describing the wrong physical system.
Driver vs. Driven
Confirm which member receives power and which member is being turned. This determines the direction of the ratio.
Whole Teeth
Use whole-number tooth counts for gears and sprockets. Decimal tooth counts are useful only as target estimates.
Idler vs. Compound Stage
Check whether an intermediate gear only changes direction or is fixed to another gear on the same shaft as part of a compound stage.
External vs. Internal Gears
If rotation direction matters, check whether the gears are external, internal, or arranged through idlers.
Torque Efficiency
Use a realistic efficiency when estimating torque. A perfect \(100\%\) value is an ideal case, not a real drivetrain assumption.
Vehicle Tire Diameter
Use measured or loaded rolling diameter when possible. Nominal tire size and actual rolling diameter may differ.
Step-by-Step Gear Ratio Examples
The most common gear ratio calculation uses driver teeth and driven teeth. The examples below also show output speed, torque, multi-stage ratio, and vehicle gearing.
Calculate Gear Ratio
Calculate Output RPM
Estimate Output Torque
Result
Gear ratio: \(3:1\). Output speed: \(1000\,rpm\). Estimated output torque: \(142.5\,N\cdot m\).
Example 2: Multi-Stage Gear Train
A compound gear train has two active stages. Stage 1 uses a 12-tooth driver and a 36-tooth driven gear. Stage 2 uses a 15-tooth driver and a 45-tooth driven gear.
If input speed is \(1800\,rpm\), final output speed is \(1800/9=200\,rpm\). This is why large reductions are often split across multiple stages instead of forced into one gear pair.
Example 3: Vehicle Speed From Gear Ratio
Suppose engine speed is \(2800\,rpm\), tire diameter is \(28\,in\), transmission ratio is \(0.70\), and axle ratio is \(3.73\).
This is a theoretical gearing estimate. It does not prove the vehicle can reach that speed because power, aerodynamic drag, traction, tire rating, slip, and road conditions are not checked.
Gear Ratio Diagrams
Diagrams help explain why a larger driven gear creates a reduction and why gear ratio trades output speed for output torque.
Typical Gear Ratio Reference Values
Practical ratios vary by application, gear type, packaging, and load. Use these ranges only as quick reference values before checking detailed design requirements.
| Application | Common Ratio Pattern | Practical Note |
|---|---|---|
| Simple spur gear pair | Often modest single-stage reductions | Very high single-stage ratios can create large center distances, small pinions, and packaging issues. |
| Robotics and small gearmotors | Frequently multi-stage reductions | High reduction improves torque but can reduce speed, increase backlash, and compound efficiency losses. |
| Bicycles and sprockets | Chainring teeth divided by rear cog teeth, depending on convention | Higher drive ratio gives more speed per pedal revolution but less climbing torque. |
| Vehicles | Transmission ratio × axle ratio | Overdrive gears may be below \(1.00:1\), while axle ratios commonly multiply the final drive effect. |
| Winches and lifting mechanisms | Usually reduction-focused | Torque, holding load, braking, duty cycle, and safety factor matter more than output speed. |
| RC cars and small drivetrains | Pinion, spur, internal ratio, and tire diameter often matter together | Changing tire diameter changes rollout and effective speed per motor revolution. |
Design Ranges and Practical Gear Checks
A mathematically correct gear ratio does not prove the design is practical. The ratio must also fit the geometry, load, speed, strength, and duty cycle of the system.
Small Tooth Counts
Very small pinions may create undercutting, poor meshing, high tooth stress, or manufacturability problems depending on gear geometry.
Large Reductions
Large reductions are often better split into multiple stages, planetary gearboxes, worm gearboxes, or other compact arrangements.
Downstream Torque
Torque multiplication can overload shafts, keys, couplings, bearings, mounts, and driven equipment even when the ratio calculation is correct.
Multi-Stage Losses
Efficiency loss and backlash can accumulate across stages, so a high total ratio may need more detailed analysis.
High Output RPM
Overdrive ratios can create high shaft speeds. Check bearings, lubrication, balance, vibration, and driven equipment limits.
Engineering judgment check
If the calculator gives a ratio that requires an extremely small driver gear, extremely large driven gear, very high rpm, or very high torque, treat the result as a concept check only. A detailed mechanical design check is needed before fabrication, equipment selection, or operation.
Gear Ratio Units and Conversions
Gear ratio itself is unitless, but the inputs used with it must be consistent. Teeth divide by teeth, diameter divides by diameter, rpm divides by ratio, and torque must be converted correctly.
| Quantity | Common Units | Conversion Reminder |
|---|---|---|
| Gear ratio | unitless, written as :1 | \(3:1\) means \(R=3\). |
| Rotational speed | rpm | Use the same rpm basis for input and output speed. |
| Torque | N·m, lb-ft, lb-in | \(1\,\mathrm{lb\cdot ft}=1.35582\,N\cdot m\); \(1\,\mathrm{lb\cdot in}=0.112985\,N\cdot m\). |
| Vehicle speed | mph, km/h | \(1\,mph=1.609344\,km/h\). |
| Tire diameter | in, mm, cm, m | Use inches with the vehicle gearing constant 336. |
Tire size note
For a tire labeled 275/70R17, sidewall height is \(275\times0.70=192.5\,mm\). Tire diameter is approximately \(17+2(192.5/25.4)=32.16\,in\), before accounting for loaded radius or tire growth.
Gear Ratio vs. Gear Reduction, Final Drive, Sprocket Ratio, and Pulley Ratio
Gear ratio, gear reduction, final drive ratio, sprocket ratio, pulley ratio, and mechanical advantage are related but not identical. The right term depends on the system and what you are trying to calculate.
| Term | What It Means | Common Use |
|---|---|---|
| Gear ratio | Driven gear teeth divided by driver gear teeth. | General gear pair and gear train calculations. |
| Sprocket ratio | Driven sprocket teeth divided by driver sprocket teeth. | Chain drives, bicycles, go-karts, motorcycles, and conveyors. |
| Pulley ratio | Driven pulley pitch diameter divided by driver pulley pitch diameter. | Belt drives, fans, blowers, pumps, and rotating machinery. |
| Gear reduction | A ratio greater than 1 that reduces speed and increases ideal torque. | Gearboxes, motors, winches, robotics, and machinery. |
| Overdrive | A ratio less than 1 that increases output speed and lowers ideal torque. | Vehicle cruising gears and speed-increase drives. |
| Final drive ratio | The effective vehicle drive ratio after transmission and axle effects. | Vehicle engine rpm, road speed, and axle ratio analysis. |
| Mechanical advantage | Force or torque multiplication from a machine. | Levers, pulleys, gears, screws, and lifting systems. |
Common Gear Ratio Mistakes
Most incorrect gear ratio results come from reversing the ratio, ignoring efficiency, or applying the formula beyond what it can physically verify.
Common Mistakes
- Dividing driver teeth by driven teeth when the intended convention is driven divided by driver.
- Assuming output torque increases without any efficiency loss.
- Using fractional tooth results as if real gears can have partial teeth.
- Assuming an idler gear changes ratio when it only changes rotation direction or spacing.
- Using outside pulley diameter when pitch diameter or effective diameter is the correct input.
- Using nominal tire diameter when loaded rolling diameter is needed for vehicle accuracy.
- Comparing vehicle axle ratios without considering transmission ratio and tire diameter.
Better Practice
- Clearly label the driver as the input member and the driven gear as the output member.
- Use realistic efficiency when estimating output torque.
- Round tooth counts to practical whole numbers and recalculate the actual ratio.
- Multiply stage ratios only when gears are part of a compound gear train.
- Use pitch diameter or effective pulley diameter for pulley ratio calculations.
- Use measured tire diameter when road-speed accuracy matters.
- Check the full drivetrain ratio before judging acceleration or cruising rpm.
Troubleshooting Unexpected Gear Ratio Results
If the result does not match your expectation, check the ratio direction, units, and whether the problem is a simple gear pair, compound gear train, or vehicle drivetrain.
| Problem | Likely Cause | Fix |
|---|---|---|
| Output speed increases when you expected reduction | Driver and driven values are probably reversed. | Use driven teeth divided by driver teeth for the ratio convention used here. |
| Torque result seems too high | Efficiency is set too high or the ratio is impractically large. | Apply realistic efficiency and check tooth strength, shafts, bearings, and heat. |
| Output torque is lower than expected | The ratio may be reversed, efficiency may be low, or losses may be larger than assumed. | Check the driver/driven convention and confirm whether efficiency represents the whole drivetrain. |
| Tooth count result is a decimal | The calculator solved an ideal target ratio, not a manufacturable gear. | Round to a whole tooth count and compare the actual ratio. |
| Vehicle speed seems unrealistic | Tire diameter, transmission ratio, axle ratio, or speed unit may be wrong. | Check tire diameter in inches, transmission gear, axle ratio, and mph vs km/h. |
| Ratio differs from a physical rotation test | An idler or compound stage may be misunderstood. | Count only active ratio-changing stages and verify which gears are fixed to the same shaft. |
| Multi-stage total ratio seems too low or too high | Stage ratios may not be multiplied correctly, or an idler may be incorrectly counted as a stage. | Only multiply active driven/driver ratios for actual compound stages. |
Assumptions, Sources, and Limitations
This calculator is intended for educational use, preliminary engineering checks, and fast ratio comparisons. It uses standard geometric ratio relationships and simplified ideal speed-torque tradeoffs.
Formula Assumption
Ratio is calculated as driven member size divided by driver member size. For gears and sprockets, the size is tooth count.
Torque Assumption
Torque calculations use a simplified efficiency multiplier and do not check strength, deflection, heat, or durability.
Vehicle Assumption
Vehicle calculations are theoretical and do not include tire growth, tire deflection, converter slip, clutch slip, traction, drag, or power limits.
Final Design Note
For final mechanical design, confirm gear geometry, bending stress, contact stress, speed limits, lubrication, shaft loads, bearings, housing design, and manufacturer data.
Calculation basis
The calculations are based on standard gear train kinematics: ratio from driven divided by driver, output speed from input speed divided by ratio, and ideal torque multiplication from ratio adjusted by efficiency. These relationships are suitable for concept checks but do not replace detailed gear design standards, AGMA-style rating checks, or manufacturer engineering data.
Gear Ratio Glossary
These terms explain the most important concepts used by the calculator.
Driver Gear
The input gear that receives power from a motor, engine, crank, or shaft.
Driven Gear
The output gear that is turned by the driver gear.
Gear Ratio
The driven member size divided by the driver member size, usually written as a ratio such as \(3:1\).
Pitch Diameter
The effective working diameter used in gear and pulley ratio calculations, depending on the drive type.
Gear Reduction
A ratio greater than 1 that reduces output speed and increases ideal output torque.
Overdrive
A ratio less than 1 that increases output speed and lowers ideal output torque.
Compound Gear Train
A multi-stage gear arrangement where gears on the same shaft create multiplied stage ratios.
Idler Gear
A gear used to change spacing or rotation direction. It usually does not change the overall ratio by itself.
Final Drive Ratio
The effective vehicle drive ratio after transmission gear ratio and axle ratio are combined.
Frequently Asked Questions
How do you calculate gear ratio?
Gear ratio is calculated by dividing the number of driven gear teeth by the number of driver gear teeth. A 60-tooth driven gear and 20-tooth driver gear gives \(60/20=3\), or a \(3:1\) gear ratio.
What does a 3:1 gear ratio mean?
A \(3:1\) gear ratio means the input turns three times for every one turn of the output. In an ideal reduction, output speed is one-third of input speed and output torque is about three times input torque before efficiency losses.
Does gear ratio increase torque?
A reduction gear ratio increases ideal output torque in proportion to the ratio, but real systems lose some torque due to friction, heat, belt slip, chain losses, bearing losses, lubrication drag, and gear mesh efficiency.
How do you calculate output RPM from gear ratio?
Output RPM is input RPM divided by gear ratio. For example, \(3000\,rpm\) through a \(3:1\) reduction gives \(3000/3=1000\,rpm\) at the output.
How do you calculate gear ratio for sprockets?
For sprockets, divide the driven sprocket tooth count by the driver sprocket tooth count. For example, a 60-tooth driven sprocket and a 20-tooth driver sprocket gives \(60/20=3:1\).
Do idler gears change gear ratio?
An idler gear normally changes rotation direction or spacing but does not change the overall gear ratio unless it is part of a compound gear train with gears fixed to the same shaft.
Can this calculator be used for final gearbox design?
The calculator is useful for ratio, RPM, torque, and vehicle gearing estimates. Final gearbox design should also check tooth strength, contact stress, lubrication, bearings, shafts, heat, backlash, manufacturability, duty cycle, safety factor, and manufacturer data.