Gear ratio calculator

How It Is Calculated

The gear ratio calculator determines how changes in tire diameter affect vehicle speed and helps you find the gear ratio needed to maintain the same speed after a tire change. The calculations follow these steps:

1. Overall gear ratio — Multiply the transmission gear ratio by the final drive ratio.
2. Current speed — Use the formula below with the current tire diameter.
3. New speed — Use the same formula with the new tire diameter.
4. Speed change — Subtract current speed from new speed.
5. Required gear ratio — Multiply the overall gear ratio by (new tire diameter / current tire diameter).

Where:

• O = overall gear ratio
• T = transmission gear ratio
• F = final drive ratio
• S = speed in mph
• R = engine RPM
• D = tire diameter in inches
• K = safety factor
• ΔS = speed change
• G = required gear ratio for same speed
• π ≈ 3.141592653589793
• 1056 = 12 in/ft × 5280 ft/mile ÷ 60 min/hr

Assumptions

• The transmission gear ratio and final drive ratio are defined as input speed divided by output speed.
• Tire diameter is measured at the tread surface in inches.
• No tire slip is considered.
• The safety factor accounts for tire wear, pressure, and measurement inaccuracies.
• The engine RPM is constant.
• The vehicle is moving in a straight line on a flat surface.
• The constant 1056 is derived from 12 inches per foot × 5280 feet per mile / 60 minutes per hour.

Worked Example

Inputs: Transmission gear ratio = 1.00, Final drive ratio = 3.73, Current tire diameter = 28 in, New tire diameter = 28 in, Engine RPM = 2000, Safety factor = 1.0

Step 1: Overall gear ratio = 1.00 × 3.73 = 3.73

Step 2: Current speed = (2000 × π × 28) / (3.73 × 1056) × 1.0 ≈ 44.7 mph

Step 3: New speed = (2000 × π × 28) / (3.73 × 1056) × 1.0 ≈ 44.7 mph

Step 4: Speed change = 44.7 − 44.7 = 0 mph

Step 5: Required gear ratio = 3.73 × (28 / 28) = 3.73

Results: Overall gear ratio = 3.73, Current speed = 44.7 mph, New speed = 44.7 mph, Speed change = 0 mph, Required gear ratio for same speed = 3.73

Practical Tips

• Measure tire diameter accurately at the tread center; a small error can change speed calculations noticeably.
• Use a safety factor below 1.0 for worn tires (e.g., 0.97) to account for reduced effective diameter.
• If you change tire size, use the required gear ratio output to select a new transmission or final drive ratio that restores your original speed.
• For electric vehicles, consider using the Motor torque calculator to ensure the motor can handle the new load.
• When adjusting gear ratios, the Bolt torque calculator can help you properly tighten drivetrain components.

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