Mechanical Advantage Calculator
Calculate ideal and actual mechanical advantage for all six simple machines: lever, pulley, wedge, screw, wheel & axle, and inclined plane. Includes efficiency and work analysis.
Gear Ratio & Speed Calculator
Calculate output speed, torque, and mechanical advantage from gear teeth counts. Supports single and compound gear trains with efficiency losses.
Stage 1
teeth
teeth
RPM
N·m
%
Gear Ratio⧉
3.000 : 1
Speed reduction / torque multiplication
Output Speed⧉
600.0 RPM
Input: 1,800 RPM
Output Torque (Ideal)⧉
30.00 N·m
Without friction losses
Output Torque (Actual)⧉
28.50 N·m
At 95% efficiency
Input Power⧉
1,885.0 W
P = τ × ω
Output Power⧉
1,790.7 W
After efficiency losses
Speed Reduction⧉
66.7%
Speed reduced
Mechanical Advantage⧉
3.000
Force multiplication factor
Speed vs Torque Trade-off
Speed
600 RPM
Torque
28.5 N·m
Common Gear Ratios Reference
| Application | Ratio | Note |
|---|---|---|
| Clock minute→hour | 12:1 | Reduction |
| Bicycle low gear | 0.82:1 | Overdrive (pedal) |
| Bicycle high gear | 4.73:1 | Reduction (wheel) |
| Car 1st gear (manual) | 3.5:1 | Torque multiplication |
| Car 5th gear (manual) | 0.8:1 | Overdrive |
| Worm gearbox | 20–100:1 | High reduction |
| Planetary gearbox | 3–10:1 | Compact reduction |
| Differential | 3–4.5:1 | Final drive |
Planning notes, formulas, and examples
About the Gear Ratio & Speed Calculator
Gear systems are one of the most fundamental mechanical power-transmission mechanisms. By meshing two gears of different sizes, you can trade speed for torque or vice versa. The gear ratio — the ratio of driven-gear teeth to driver-gear teeth — determines exactly how much the output speed decreases and the torque increases (or the reverse for an overdrive arrangement).
This Gear Ratio & Speed Calculator lets you enter the number of teeth on the driver (input) and driven (output) gears, along with the input speed in RPM, to compute the output speed, torque multiplication, and mechanical advantage. It also supports compound (two-stage) gear trains for higher reduction ratios, and accounts for real-world efficiency losses.
Whether you are designing a gearbox for a robot, selecting sprockets for a bicycle, sizing a speed reducer for an industrial motor, or studying gear mechanics in a physics class, This calculator gives you all the key numbers in one place. Explore common preset configurations, review the reference table of typical gear ratios, and visualize the speed-torque trade-off with interactive bar charts.
When This Page Helps
Manually calculating gear ratios involves dividing tooth counts, then propagating the result through torque and power equations — a process that grows tedious for compound trains. This calculator automates the entire chain: gear ratio, output RPM, ideal and actual torque, input and output power, and mechanical advantage. It also includes an efficiency parameter to model real friction losses, which textbook formulas often ignore.
The preset buttons let you explore real-world scenarios — from bicycle drivetrains to industrial worm gears — so you can build intuition for how different gear configurations behave.
How to Use the Inputs
- Select single-stage or compound (two-stage) configuration.
- Enter the number of teeth on the driver (input) gear.
- Enter the number of teeth on the driven (output) gear.
- For compound trains, enter the Stage 2 driver and driven teeth as well.
- Enter the input speed in RPM and input torque in N·m.
- Adjust the efficiency percentage to model friction losses (default 95%).
- Read the output speed, torque, power, and mechanical advantage from the results.
Formula used
Gear Ratio:
GR = N_driven / N_driver
Output Speed:
RPM_out = RPM_in / GR
Output Torque (ideal):
τ_out = τ_in × GR
Actual Torque:
τ_actual = τ_out × η
Power:
P = τ × ω = τ × (2πn / 60)
Compound Ratio:
GR_total = GR₁ × GR₂Example Calculation
Result: 600 RPM output, 28.5 N·m actual torque
With 20 driver teeth and 60 driven teeth, the gear ratio is 3:1. The input speed of 1,800 RPM is reduced to 600 RPM. Ideal output torque is 30 N·m (3 × 10), and at 95% efficiency the actual torque is 28.5 N·m.
Tips & Best Practices
- For high reduction ratios, use compound trains instead of very large single-stage ratios to keep gear sizes practical.
- Worm gears can achieve 40:1 or higher in a single stage but have lower efficiency (50–90%).
- Match the gear module (metric) or diametral pitch (imperial) between meshing gears.
- Helical gears run quieter than spur gears but introduce axial thrust loads.
- Always factor in efficiency losses — they compound across multiple stages.
Understanding Gear Systems
Gears are toothed wheels that mesh together to transmit rotary motion and force. The fundamental trade-off is between speed and torque: when you decrease speed through a gear reduction, you proportionally increase torque (minus efficiency losses). This principle applies whether you are designing a clock mechanism, a car transmission, or an industrial conveyor drive.
Types of Gear Configurations
**Spur gears** have straight teeth and are the simplest and most common type. They work well for parallel-shaft applications. **Helical gears** have angled teeth, producing smoother, quieter operation but generating axial thrust. **Bevel gears** transmit motion between intersecting shafts, commonly at 90°. **Worm gears** use a screw-like worm meshing with a worm wheel to achieve very high single-stage reductions and self-locking behavior. **Planetary (epicyclic) gear sets** arrange gears concentrically for compact, high-ratio reductions used in automatic transmissions and robotics.
Practical Applications
Gear ratio calculations are essential in automotive engineering (transmission gear selection), robotics (motor-to-joint speed matching), manufacturing (spindle drives), cycling (chainring/sprocket selection), and aerospace (turbine reduction gearboxes). Understanding the speed-torque-power relationship through the gear ratio is fundamental to mechanical design.
Sources & Methodology
Last updated:
Frequently Asked Questions
A gear ratio is the ratio of the number of teeth on the driven gear to the number of teeth on the driver gear. It determines how much the output speed and torque change relative to the input.
A gear ratio greater than 1 reduces output speed but increases torque by the same factor (minus friction losses). A ratio less than 1 is an overdrive — speed increases but torque decreases.
A compound gear train has two or more gear pairs in series, typically sharing a common shaft between stages. The total gear ratio is the product of the individual stage ratios, allowing very high reductions in a compact package.
Real gears lose energy to friction at the tooth contact surfaces, in bearings, and through lubricant churning. Typical spur-gear efficiency is 95–98% per stage; worm gears may be 50–90%. Including efficiency gives realistic torque and power values.
Yes. Enter the chainring teeth as the driver and the sprocket teeth as the driven gear. The presets include typical bicycle low and high gear configurations.
Standard spur gears are available with tooth counts from about 10 to over 100. Smaller gears with fewer teeth may suffer from undercutting. Standard module or diametral-pitch gears ensure interchangeable mesh when the module matches.
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