# Uniform acceleration: Calculator & Formulas

Diese Seite auf Deutsch: Be­schleu­nigungs­rechner

By default, this online acceleration calculator computes the uniform acceleration for the speed reached in a given time. It does not use the well-known rules of thumb from driving school. Instead, the calculation is performed with the exact formulas from physik which can be found below the calculator.

By default, the mean acceleration from 0 to 100 km/h in a time of 3 seconds and the required distance are calculated. Of course the default values can be changed at any time.

## Acceleration Calculator for Road & Rail

Under „vehicle choice“ you will find suitable values for road and rail vehicles.

 vehicle choice    sports car mid-range car bicyclist underground time * s
 initial speed km/h final speed * km/h
 distance m
 acceleration** m/s²

* This value is automatically entered by selecting the vehicle, can be changed as required anytime!

** Mean acceleration. For deceleration set a minus in front of the number!

Further functions: Enter a number in three of the five fields and press calculate!

### Manual

• This calculator computes the following, whereby exactly three of the five quanties must be known:
• Stopping (braking) distance or acceleration distance
• Acceleration or deceleration
• Braking time
• Initial speed
• Final speed
• The calculation is valid for uniform acceleration or constant deceleration only.
• Accuracy can not be guaranteed – for corrections or additions please use my contact form!

## Numerical Values for the Acceleration

 Example Accelerationin m/s² bicyclist – mean acceleration 0 – 20 km/h 1 mid-range car – mean acceleration 0 – 100 km/h 3 sports car – mean acceleration 0 – 100 km/h 9 underground Vienna – mean acceleration 0 – 40 km/h 1.25 tram Vienna (ULF) – mean acceleration 1.3 ÖBB 4020 (city train Vienna) – starting acceleration 0.7 Siemens Desiro ML, ÖBB 5022 – starting acceleration 1.1 acceleration of gravity 9.81

## Formulas for Calculating the Mean Acceleration

 mean acceleration a with starting velocity $$\frac{v – v_0}{t}$$ $$\frac{2·s}{t^2} – \frac{2·v_0}{t}$$ $$\frac{v^2 – v_0^2}{2·s}$$ $$\frac{2·v}{t} – \frac{2·s}{t^2}$$ without starting velocity (v0 = 0) $$\frac{v}{t}$$ $$\frac{2·s}{t^2}$$ $$\frac{v^2}{2·s}$$

 a: acceleration in m/s² v0: starting velocity in m/s v: final velocity in m/s s: distance in m t: times in s

### Simple Example

#### Specification

A car needs 5 seconds to reach a speed of 100 km/h. What is the mean acceleration?

#### Solution

First you have to convert 100 km/h in m/s. Just divide 100 by 3.6: 100/3.6 = 27.7 m/s. Then take the formula in the 2nd column, 3rd line and plug in the values:

$$a = \frac{v}{t} = \frac{27.\overline 7}{5} = 5.\overline 5\ \frac{m}{s^2}$$

The mean acceleration from 0 to 100 km/h is about 5.6 m/s².

Page created on 07 June 2019. Last change: 20 November 2021.