Speed / Gear Ratio Equation
Links vehicle speed to engine RPM, tire radius, and the final drive gear ratio. The constant 168 handles unit conversion from inches and RPM to miles per hour. Solve for any one variable when you know the other three.
v = (r × RPM) / (168 × G)
Effective Gear Ratio Equation
Shows how a tire-size change alters your gearing. When you install larger tires, the effective gear ratio drops, lowering RPM at highway speed and potentially hurting acceleration.
G_e = (d_old / d_new) × G
Tire Diameter Equation
Converts metric tire sizes (e.g., 225/65R17) to inches. Section width (W) is in millimeters, aspect ratio (A) is a decimal, and rim diameter (d_r) is in inches.
d = (2 × W × A) / 25.4 + d_r
Crawl Ratio Equation
Multiplies the differential, transfer case, and transmission ratios to find the overall low-range reduction for off-road driving. Higher crawl ratios provide more torque at the wheels for rock crawling.
C = D × T × G_t
How It Works
The gear equation links vehicle speed to engine RPM, tire size, and the final drive gear ratio. The constant 168 handles the unit conversion from inches and RPM to miles per hour (63,360 in/mi ÷ 60 min/hr ÷ 2π). The effective gear ratio shows how a tire-size change alters your gearing. The tire diameter equation converts metric tire sizes to inches. The crawl ratio multiplies the differential, transfer case, and transmission ratios to find the overall low-range reduction for off-road driving.
Example Problem
A truck with 15-inch tire radius, 3.73 gear ratio, cruising at 3,000 RPM. What is the speed?
- Speed = (15 × 3,000) / (168 × 3.73)
- Speed = 45,000 / 626.64 = 71.8 mph
When to Use Each Variable
- Solve for Speed — when you know tire radius, RPM, and gear ratio, e.g., predicting highway speed at a given engine RPM.
- Solve for RPM — when you know speed, tire radius, and gear ratio, e.g., finding engine RPM at a target cruising speed.
- Solve for Gear Ratio — when you know speed, RPM, and tire size, e.g., choosing a differential ratio for a desired RPM at highway speed.
- Solve for Effective Gear Ratio — when comparing old and new tire sizes, e.g., seeing how a tire upgrade changes your effective gearing.
- Solve for Tire Diameter — when converting a metric tire size (e.g., 225/65R17) to inches for gear calculations.
- Solve for Crawl Ratio — when multiplying differential, transfer case, and transmission ratios, e.g., evaluating off-road low-range capability.
Key Concepts
The gear ratio equation links engine RPM to vehicle speed through tire size and the final drive ratio. The constant 168 converts inches and RPM to miles per hour. The effective gear ratio shows how a tire-size change alters gearing — larger tires lower the effective ratio, reducing RPM at highway speed. The crawl ratio multiplies all drivetrain ratios to determine the overall mechanical advantage in low range.
Applications
- Off-road vehicles: calculating crawl ratios to ensure sufficient low-speed torque for rock crawling
- Drag racing: selecting gear ratios to keep the engine in its power band through the quarter-mile
- Fleet management: choosing differential ratios that balance fuel economy and towing capacity
- Tire upgrades: predicting the effect of larger tires on speedometer accuracy and engine RPM
Common Mistakes
- Using tire diameter instead of tire radius in the speed formula — the equation requires radius (half the diameter)
- Forgetting to include both transmission and differential ratios — the gear ratio in the formula is the overall (combined) ratio
- Not re-gearing after a tire size change — larger tires lower the effective ratio, hurting acceleration and causing transmission hunting
- Ignoring drivetrain losses — the formula assumes no slip or friction losses in the drivetrain
Frequently Asked Questions
What happens if I install larger tires without re-gearing?
Larger tires lower your engine RPM at highway speed, which can hurt low-end acceleration and cause the transmission to hunt between gears. Re-gearing to a numerically higher ratio (e.g., 3.73 to 4.10) restores the original RPM range.
What is a good gear ratio for fuel economy?
Lower ratios like 2.73:1 or 3.08:1 keep RPM down at highway speed, improving fuel economy. However, they sacrifice acceleration. The best ratio depends on tire size and the engine’s torque curve.
Does this formula account for transmission gears?
The gear ratio here is the overall ratio (transmission gear × differential ratio). In top gear (often 1:1 or an overdrive like 0.7:1), the effective ratio equals the differential ratio multiplied by the transmission gear.
Reference: Results are approximate and assume no drivetrain losses or tire slip.
Related Calculators
- Horsepower Calculator — HP, torque, and RPM.
- Engine Equations Calculator — volumetric efficiency and displacement.
- Torque Calculator — calculate torque from force and lever arm.
- Tire Size Comparison Calculator — compare tire dimensions that affect final drive ratio.
- Speed Unit Converter — convert between mph, km/h, m/s, and other speed units.
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Note: Results are approximate and assume no drivetrain losses or tire slip.