Calculate Gear Ratio
Enter the number of teeth on each gear to calculate the gear ratio, output RPM, and torque. Supports single-stage and multi-stage gear trains.
| Stage | Driving | Driven | Ratio | RPM Out | Torque Out |
|---|
Common Gear Ratios Reference
Here are typical gear ratios used in various applications:
Automotive Transmissions
| Gear | Typical Ratio | Purpose |
|---|---|---|
| 1st | 2.5:1 -- 4.0:1 | Maximum torque for starting from rest |
| 2nd | 1.5:1 -- 2.5:1 | Acceleration at low-medium speed |
| 3rd | 1.0:1 -- 1.5:1 | Moderate speed driving |
| 4th | 0.7:1 -- 1.0:1 | Direct drive or slight overdrive |
| 5th/6th | 0.5:1 -- 0.8:1 | Overdrive for fuel economy at highway speed |
| Reverse | 2.5:1 -- 4.0:1 | Similar to 1st gear for low-speed maneuvering |
| Final drive | 3.0:1 -- 4.5:1 | Differential ratio multiplied with gear ratio |
Bicycle Gears
| Combination | Chainring / Cog | Ratio | Use |
|---|---|---|---|
| Lowest (climbing) | 30T / 36T | 0.83:1 | Steep hill climbing |
| Low | 34T / 28T | 1.21:1 | Moderate climbs |
| Medium | 39T / 17T | 2.29:1 | Flat road cruising |
| High | 50T / 14T | 3.57:1 | Fast flat riding |
| Highest (sprinting) | 53T / 11T | 4.82:1 | Maximum speed on flat/downhill |
Industrial & Other Applications
| Application | Typical Ratio | Notes |
|---|---|---|
| Worm gear (single start) | 20:1 -- 100:1 | High reduction, often self-locking |
| Planetary gearbox | 3:1 -- 10:1 per stage | Compact, coaxial input/output |
| Clock mechanism | 12:1 (hour to minute) | Minute hand 12x faster than hour hand |
| Winch / hoist | 30:1 -- 300:1 | Very high torque for lifting loads |
| Drill press | 1:1 -- 5:1 | Variable speed via belt/pulley or gears |
| Lathe spindle | 0.5:1 -- 6:1 | Wide range for different materials and diameters |
| Wind turbine gearbox | 50:1 -- 100:1 | Steps up slow blade RPM to generator speed |
Gear Ratio Formulas
Basic gear ratio
Gear Ratio = Driven Teeth / Driving Teeth
Output RPM
Output RPM = Input RPM / Gear Ratio
Output torque
Output Torque = Input Torque x Gear Ratio x Efficiency
Multi-stage overall ratio
Overall Ratio = Ratio_1 x Ratio_2 x ... x Ratio_n
In a multi-stage gear train, each stage multiplies the ratio of the previous stage. This is how very high reduction ratios (e.g., 100:1 or more) are achieved in compact assemblies. Each stage also introduces some friction loss, which is why the efficiency input is applied per stage.
Examples
Example 1 -- Simple speed reduction
Setup: Motor with a 15-tooth pinion driving a 60-tooth gear at 3000 RPM, 5 Nm torque
- Gear ratio = 60 / 15 = 4:1
- Output RPM = 3000 / 4 = 750 RPM
- Output torque = 5 x 4 = 20 Nm (at 100% efficiency)
- This is a speed reducer -- output is slower but 4x stronger
Example 2 -- Speed increase (overdrive)
Setup: 50-tooth gear driving a 25-tooth gear at 1000 RPM
- Gear ratio = 25 / 50 = 0.5:1
- Output RPM = 1000 / 0.5 = 2000 RPM
- Output spins 2x faster, but torque is halved
Example 3 -- Two-stage gear train
Setup: Stage 1: 12T drives 48T. Stage 2: 10T drives 50T. Input: 1800 RPM, 8 Nm.
- Stage 1 ratio = 48 / 12 = 4:1
- Stage 2 ratio = 50 / 10 = 5:1
- Overall ratio = 4 x 5 = 20:1
- Output RPM = 1800 / 20 = 90 RPM
- Output torque = 8 x 20 = 160 Nm (at 100% efficiency)
- At 95% efficiency per stage: 160 x 0.95 x 0.95 = 144.4 Nm
Understanding Gear Ratios
What is a gear ratio?
A gear ratio describes the relationship between two meshing gears. It tells you how many times the driving gear (input) must rotate for the driven gear (output) to complete one rotation. A 3:1 ratio means the driving gear turns 3 times for every 1 turn of the driven gear.
Speed versus torque tradeoff
Gears obey the law of conservation of energy. When gears reduce speed, they proportionally increase torque, and vice versa. This is the fundamental tradeoff in all gear systems:
- Ratio greater than 1:1 -- Output is slower but has more torque (speed reduction / torque multiplication)
- Ratio equal to 1:1 -- No change in speed or torque (direct drive)
- Ratio less than 1:1 -- Output is faster but has less torque (speed increase / overdrive)
Why use multi-stage gear trains?
Single gear pairs are limited in practical ratio. A very large driven gear paired with a very small driving gear becomes unwieldy. Multi-stage trains solve this by cascading multiple modest ratios. For example, two 5:1 stages give a compact 25:1 overall ratio, which would require an impractically large gear in a single stage.
Efficiency and friction
Real gears lose some energy to friction, heat, and noise. Spur gears are typically 95-98% efficient per mesh. Helical gears are similar. Worm gears can be as low as 40-90% efficient depending on the lead angle. Each stage in a multi-stage train multiplies the losses, so a 3-stage train at 95% per stage has an overall efficiency of about 85.7%.
Practical considerations
- Module / pitch: Meshing gears must have the same module (metric) or diametral pitch (imperial) to mesh correctly
- Center distance: Determined by the sum of pitch radii of the two gears
- Backlash: Small clearance between teeth; important for smooth operation but introduces play
- Direction of rotation: External gear pairs reverse direction; internal (ring) gears maintain direction
- Idler gears: Change direction without affecting ratio (same number of teeth in, same out)
Frequently Asked Questions
What is a gear ratio?
A gear ratio is the relationship between the number of teeth on two meshing gears. It is calculated by dividing the driven gear teeth by the driving gear teeth. A ratio of 3:1 means the output turns once for every 3 turns of the input, giving 3 times the torque at one-third the speed.
How do I calculate gear ratio?
Divide the number of teeth on the driven (output) gear by the number of teeth on the driving (input) gear. For example, a 20-tooth driver meshing with a 60-tooth driven gear gives 60/20 = 3:1.
How does gear ratio affect RPM?
Output RPM equals input RPM divided by the gear ratio. A 3:1 ratio with 3000 RPM input gives 1000 RPM output. Conversely, a 0.5:1 ratio doubles the output speed.
How does gear ratio affect torque?
Output torque equals input torque multiplied by the gear ratio (and by efficiency). A 3:1 ratio triples the torque. This is how vehicles achieve high wheel torque from relatively small engines.
What is a multi-stage gear train?
A multi-stage gear train uses two or more gear pairs in series. The overall ratio is the product of individual stage ratios. This allows achieving very high ratios in a compact space. For example, three stages of 4:1 give 64:1 overall.
What is the difference between speed reduction and overdrive?
Speed reduction (ratio > 1) slows the output but increases torque -- used for climbing hills, heavy loads, or starting. Overdrive (ratio < 1) speeds up the output but reduces torque -- used for highway cruising or high-speed operation.
Does this calculator account for friction losses?
Yes. Use the efficiency input to model real-world losses. Set it to 95-98% for spur and helical gears, or 40-90% for worm gears. The default of 100% gives ideal (theoretical) results.
Does this calculator store my data?
No. All calculations run entirely in your browser. No data is sent to any server, and nothing is stored.
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- Moment of Inertia Calculator -- calculate moment of inertia for common shapes
Privacy
This calculator runs entirely in your browser. No data is transmitted or stored anywhere. All gear ratio, RPM, and torque calculations happen client-side using JavaScript.
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Gear Ratio Calculator FAQ
What is a gear ratio?
A gear ratio is the relationship between the number of teeth on two meshing gears. It is calculated by dividing the number of teeth on the driven gear by the number of teeth on the driving gear. For example, if the driving gear has 20 teeth and the driven gear has 40 teeth, the gear ratio is 2:1.
How do I calculate gear ratio?
Gear ratio = Driven gear teeth / Driving gear teeth. For example, a 15-tooth driving gear meshing with a 45-tooth driven gear gives a ratio of 45/15 = 3:1. This means the driven gear rotates 3 times slower but with 3 times more torque.
How does gear ratio affect RPM?
Output RPM = Input RPM / Gear Ratio. A gear ratio greater than 1 reduces speed (and increases torque). A gear ratio less than 1 increases speed (and reduces torque). For example, with a 3:1 ratio and 3000 RPM input, the output is 1000 RPM.
How does gear ratio affect torque?
Output Torque = Input Torque x Gear Ratio. A gear ratio greater than 1 multiplies torque. For example, a 3:1 ratio with 10 Nm input torque produces 30 Nm output torque (ignoring friction losses).
What is a multi-stage gear train?
A multi-stage gear train uses two or more pairs of meshing gears in series. The overall gear ratio is the product of each individual stage ratio. This allows achieving very high or very low ratios that would be impractical with a single gear pair.
What is the difference between speed reduction and speed increase?
Speed reduction (ratio > 1) occurs when the driven gear has more teeth than the driving gear. The output spins slower but with more torque. Speed increase (ratio < 1) is the opposite -- the driven gear has fewer teeth, so it spins faster but with less torque.
Does this calculator account for friction losses?
The calculator provides an optional efficiency input (default 100%). Real-world gear systems typically have 90-98% efficiency per stage depending on gear type. You can adjust the efficiency to see realistic torque output.
Does this calculator store my data?
No. All calculations run entirely in your browser. No data is sent to any server, and nothing is stored.