Gear Ratio Calculator
Calculate gear ratio accurately for your build. Get material quantities, waste allowances, and project cost breakdowns.
Formula
Gear Ratio = Driven Teeth / Driving Teeth | Output RPM = Input RPM / Ratio | Output Torque = Input Torque ร Ratio ร ฮท
The gear ratio equals the number of teeth on the driven gear divided by the driving gear teeth. Output RPM is inversely proportional to the ratio, while output torque is directly proportional (multiplied by the efficiency factor ฮท). Power is conserved minus friction losses.
Worked Examples
Example 1: Motor Speed Reduction
Problem: A 1750 RPM motor with a 15-tooth pinion drives a 75-tooth gear. The motor produces 10 Nยทm of torque. Calculate outputs at 95% efficiency.
Solution: Gear Ratio = 75/15 = 5:1\nOutput RPM = 1750 / 5 = 350 RPM\nOutput Torque = 10 ร 5 ร 0.95 = 47.5 Nยทm\nInput Power = 10 ร 1750 ร 2ฯ/60 = 1,832.6W = 2.46HP\nOutput Power = 1,832.6 ร 0.95 = 1,740.9W
Result: Ratio = 5:1 | Output = 350 RPM | Torque = 47.5 Nยทm | 2.46HP
Example 2: Bicycle Gear Analysis
Problem: A bicycle has a 44-tooth chainring driving a 16-tooth rear sprocket. The cyclist pedals at 80 RPM with 40 Nยทm of torque.
Solution: Gear Ratio = 16/44 = 0.364 (speed increase)\nOutput RPM = 80 / 0.364 = 220 RPM (wheel turns faster)\nOutput Torque = 40 ร 0.364 ร 0.97 = 14.1 Nยทm\nThis is a speed-increasing setup (ratio < 1)\nWheel turns 2.75ร faster than pedals
Result: Ratio = 0.364:1 | Wheel = 220 RPM | Torque = 14.1 Nยทm
Frequently Asked Questions
What is a gear ratio?
A gear ratio is the relationship between the number of teeth on two meshing gears, expressed as the ratio of driven gear teeth to driving gear teeth. It determines how speed and torque are transferred between gears. A gear ratio greater than 1 means speed reduction and torque multiplication (the output shaft turns slower but with more force). A gear ratio less than 1 means speed increase and torque reduction. For example, a 60-tooth driven gear meshing with a 20-tooth driving gear gives a 3:1 ratio, meaning the output turns 3 times slower but with 3 times the torque.
How does gear ratio affect torque and speed?
Gear ratio creates an inverse relationship between speed and torque: Speed reduction = torque multiplication, and speed increase = torque reduction. Output RPM = Input RPM / Gear Ratio. Output Torque = Input Torque x Gear Ratio x Efficiency. In an ideal (100% efficient) system, power is conserved: P = Torque x RPM. In reality, friction losses reduce efficiency to typically 95-98% per gear stage. This trade-off is fundamental to mechanical design, allowing engineers to match motor characteristics to load requirements.
What is the difference between gear ratio and speed ratio?
Gear ratio and speed ratio are reciprocals of each other. Gear ratio = Driven teeth / Driving teeth = Input speed / Output speed. Speed ratio = Driving teeth / Driven teeth = Output speed / Input speed. For example, if a 20-tooth gear drives a 60-tooth gear: Gear ratio = 60/20 = 3:1 (output is 3x slower), Speed ratio = 20/60 = 1:3 (output is 1/3 the speed). Engineers typically use gear ratio when discussing torque multiplication and speed ratio when discussing velocity changes.
How do I calculate compound gear train ratios?
For a compound gear train (multiple gear pairs on shared shafts), the overall gear ratio is the product of individual pair ratios. For a two-stage train: Total Ratio = (Driven1/Driving1) x (Driven2/Driving2). For example: Stage 1: 20-tooth drives 60-tooth (3:1), Stage 2: 15-tooth drives 45-tooth (3:1). Total ratio = 3 x 3 = 9:1. The output turns 9 times slower with 9 times the torque. Compound trains allow high ratios in compact space. Each stage adds friction losses (typically 2-5% per mesh), so a 3-stage train at 97% per stage has 91.3% overall efficiency.
Is my data stored or sent to a server?
No. All calculations run entirely in your browser using JavaScript. No data you enter is ever transmitted to any server or stored anywhere. Your inputs remain completely private.
How do I interpret the result?
Results are displayed with a label and unit to help you understand the output. Many calculators include a short explanation or classification below the result (for example, a BMI category or risk level). Refer to the worked examples section on this page for real-world context.