Steering Ratio Calculator

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Front Axle and Steering

Driveline

Race Car Vehicle Dynamics

Suspension Geometry

Vehicle Collision

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Steering System

Moments, Loads, Angles acting on Steering system and Axles

Movement Ratio

Pivot Centre, Wheel Base and Track

Turning Radius

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Angles Related to Steering System

✖Steering Wheel Radius is the radius of the steering wheel which is controlled by the driver.ⓘ Steering Wheel Radius [R]			+10% -10%
✖Pinion Pitch Circle Radius is the radius of the pinion of the rack and pinion steering system.ⓘ Pinion Pitch Circle Radius [r]			+10% -10%

✖Steering Ratio refers to the ratio between the turn of the steering wheel and the turn of the wheels.ⓘ Steering Ratio [S_r]

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Formula

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Steering Ratio

Formula

`"S"_{"r"} = "R"/"r"`

Example

`"23.33333"="350mm"/"15mm"`

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Steering Ratio Solution

STEP 0: Pre-Calculation Summary

Formula Used

Steering Ratio = Steering Wheel Radius/Pinion Pitch Circle Radius
S_r = R/r
This formula uses 3 Variables

Variables Used

Steering Ratio - Steering Ratio refers to the ratio between the turn of the steering wheel and the turn of the wheels.
Steering Wheel Radius - (Measured in Meter) - Steering Wheel Radius is the radius of the steering wheel which is controlled by the driver.
Pinion Pitch Circle Radius - (Measured in Meter) - Pinion Pitch Circle Radius is the radius of the pinion of the rack and pinion steering system.

STEP 1: Convert Input(s) to Base Unit

Steering Wheel Radius: 350 Millimeter --> 0.35 Meter (Check conversion here)
Pinion Pitch Circle Radius: 15 Millimeter --> 0.015 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

S_r = R/r --> 0.35/0.015

Evaluating ... ...

S_r = 23.3333333333333

STEP 3: Convert Result to Output's Unit

23.3333333333333 --> No Conversion Required

FINAL ANSWER

23.3333333333333 ≈ 23.33333 <-- Steering Ratio

(Calculation completed in 00.004 seconds)

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Home » Physics » Automobile » Front Axle and Steering » Steering System » Steering Ratio

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Created by Syed Adnan

Ramaiah University of Applied Sciences (RUAS), bangalore

Syed Adnan has created this Calculator and 200+ more calculators!

Verified by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

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< 6 Steering System Calculators

Understeer Gradient

Go Understeer Gradient = (Load on Front Axle at High Speed Cornering/(Acceleration due to Gravity*Cornering Stiffness of Front Wheels))-(Load on Rear Axle at High Speed Cornering/(Acceleration due to Gravity*Cornering Stiffness of Rear Wheels))

Understeer Increment due to Steering System Compliance

Go Under Steer Increment due to Steering Compliance = (Weight under Front Axle*(Turning Radius of Car*Caster Angle+Pneumatic Trail of Tire))/Effective Stiffness of Steering System

Pinion Pitch Circle Radius

Go Pinion Pitch Circle Radius = (Number of Pinion Teeth*Linear or Circular Pitch)/(2*pi)

Steering Ratio

Go Steering Ratio = Steering Wheel Radius/Pinion Pitch Circle Radius

Motion Ratio or Installation Ratio in Suspension

Go Motion Ratio in Suspension = Spring/Shock Travel/Wheel Travel

Torque Acting on Steering Arm

Go Torque = Frictional Force*Scrub Radius

Steering Ratio Formula

Steering Ratio = Steering Wheel Radius/Pinion Pitch Circle Radius
S_r = R/r

What is steering ratio?

Steering ratio is a ratio of the degrees of steering wheel angle input and degrees of road wheel toe angle change.

Steering ratio is a function of rack ratio (mm of rack travel per steering wheel revolution) and suspension geometry. The primary suspension geometry measure is steering lever arm length. Steering arm length is the shortest distance between the suspension steer axis and the steering rack attachment to the wheel carrier.

How to Calculate Steering Ratio?

Steering Ratio calculator uses Steering Ratio = Steering Wheel Radius/Pinion Pitch Circle Radius to calculate the Steering Ratio, The Steering ratio formula is defined as ratio of the degrees of steering wheel angle input and degrees of road wheel toe angle change. Steering Ratio is denoted by S_r symbol.

How to calculate Steering Ratio using this online calculator? To use this online calculator for Steering Ratio, enter Steering Wheel Radius (R) & Pinion Pitch Circle Radius (r) and hit the calculate button. Here is how the Steering Ratio calculation can be explained with given input values -> 23.33333 = 0.35/0.015.

FAQ

What is Steering Ratio?

The Steering ratio formula is defined as ratio of the degrees of steering wheel angle input and degrees of road wheel toe angle change and is represented as S_r = R/r or Steering Ratio = Steering Wheel Radius/Pinion Pitch Circle Radius. Steering Wheel Radius is the radius of the steering wheel which is controlled by the driver & Pinion Pitch Circle Radius is the radius of the pinion of the rack and pinion steering system.

How to calculate Steering Ratio?

The Steering ratio formula is defined as ratio of the degrees of steering wheel angle input and degrees of road wheel toe angle change is calculated using Steering Ratio = Steering Wheel Radius/Pinion Pitch Circle Radius. To calculate Steering Ratio, you need Steering Wheel Radius (R) & Pinion Pitch Circle Radius (r). With our tool, you need to enter the respective value for Steering Wheel Radius & Pinion Pitch Circle Radius and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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