Authoritative Source & Methodology

This calculator uses fundamental principles of mechanical engineering and vehicle dynamics. The formulas are standardized and rigorously cross-referenced against authoritative texts.

  • Authoritative Data Source: "Bosch Automotive Handbook", 10th Edition.
  • Reference: Chapter on "Vehicle Dynamics" and "Powertrain".
  • Publisher: Robert Bosch GmbH.

All calculations are strictly based on the fundamental engineering formulas and definitions provided by this source.

The Formulas Explained

The calculator uses three core formulas to determine the results.

1. Simple Gear Ratio

The ratio between two gears is found by dividing the number of teeth on the driven gear by the number of teeth on the driving gear.

$$ \text{Gear Ratio} = \frac{T_{\text{driven}}}{T_{\text{driving}}} $$

2. Final Drive Ratio (FDR)

The FDR is the total gear reduction from the engine to the wheels. It's calculated by multiplying the transmission's current gear ratio by the axle's (differential) ratio.

$$ \text{FDR} = R_{\text{transmission}} \times R_{\text{axle}} $$

3. Vehicle Speed (MPH)

Vehicle speed is calculated by determining the wheel's rotational speed (based on engine RPM and FDR) and multiplying it by the tire's circumference. The constant 336.13 simplifies the conversion of inches-per-minute to miles-per-hour.

$$ \text{Speed (MPH)} = \frac{\text{RPM} \times D_{\text{tire}}}{\text{FDR} \times 336.13} $$

For KPH, the result is multiplied by 1.60934.

Glossary of Variables

  • Tdriving (Driving Gear Teeth): The number of teeth on the input gear (e.g., connected to the motor).
  • Tdriven (Driven Gear Teeth): The number of teeth on the output gear.
  • RPM (Engine RPM): Engine revolutions per minute, as shown on your tachometer.
  • Dtire (Tire Diameter): The total height of the tire in inches.
  • Raxle (Axle Ratio): The fixed gear ratio inside the differential (e.g., 3.73:1 is entered as 3.73).
  • Rtransmission (Transmission Ratio): The ratio of the currently selected gear (e.g., 1.0 for a 1:1 gear, or 0.67 for an overdrive gear).
  • FDR (Final Drive Ratio): The total gear reduction applied to the engine's RPM.

How It Works: A Step-by-Step Example

Let's calculate the speed of a car with the following parameters:

  • Engine RPM: 3500 RPM
  • Tire Diameter: 27 inches
  • Axle Ratio: 4.10:1 (Use 4.10)
  • Transmission Ratio: 0.70:1 (An overdrive gear. Use 0.70)

Step 1: Calculate the Final Drive Ratio (FDR)

Using the FDR formula, we multiply the transmission and axle ratios.

FDR = 0.70 × 4.10 = 2.87

Step 2: Calculate the Vehicle Speed in MPH

Using the speed formula, we plug in our numbers.

Speed (MPH) = (3500 × 27) / (2.87 × 336.13)

Speed (MPH) = 94500 / 964.6931

Speed (MPH) ≈ 97.96

At 3500 RPM in this gear, the vehicle would be traveling at approximately 98 MPH.

Frequently Asked Questions

What is a gear ratio?

A gear ratio is a mechanical ratio that defines the relationship between the rotational speeds of two or more gears. A 4:1 ratio means the driving (input) gear must turn 4 times to make the driven (output) gear turn once, resulting in higher torque but lower speed.

What does a "high" vs. "low" gear ratio mean?

This can be confusing. A 'low gear' (like 1st gear) has a numerically high ratio (e.g., 4.10:1) and provides high torque for acceleration. A 'high gear' (like 6th gear) has a numerically low ratio (e.g., 0.67:1) and provides high speed at lower RPM for fuel efficiency.

How do I find my tire diameter?

You can measure it directly or calculate it from the tire's sidewall code (e.g., 265/70R17). We recommend using a dedicated 'Tire Size Calculator' for the most accurate diameter in inches.

What is the difference between axle ratio and transmission ratio?

The transmission ratio is the gear you are currently in (1st, 2nd, etc.). The axle ratio (or differential ratio) is a fixed ratio in the differential that provides a final stage of torque multiplication before the wheels. Your total 'Final Drive Ratio' is the transmission ratio multiplied by the axle ratio.

Why does gear ratio affect fuel economy?

Gearing determines how hard the engine must work (RPM) to maintain a certain speed. A numerically low 'highway gear' (overdrive) allows the engine to spin at a lower, more efficient RPM while cruising, thus saving fuel. A high numerical ratio (low gear) forces the engine to spin faster, using more fuel but providing more power.

Can I calculate RPM from speed?

Yes, you can rearrange the speed formula to solve for RPM: RPM = (Speed × FDR × 336.13) / Tire Diameter. This tool is designed to calculate speed from RPM, but you can use this formula manually to find the reverse.

Tool developed by Ugo Candido.
Automotive engineering content verified by the CalcDomain Editorial Board.

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