Calculate braking acceleration, stopping distance, or velocity before braking when you enter any two values in m/s, km/h, mph, or ft/s.
- All Automotive Calculators
- All Acceleration Calculators
- Braking Force Calculator
- Stopping Distance Calculator
- Brake Caliper Clamping Force Calculator
Braking Acceleration Formula
The braking acceleration calculator uses the constant-acceleration stopping equation. It assumes the final velocity is 0, meaning the object comes to a complete stop.
a = v^2/(2d)
d = v^2/(2a)
v = sqrt(2ad)
- a = braking acceleration, usually treated as a positive deceleration value
- v = velocity before braking
- d = total stopping distance
The calculator lets you enter any two of the three values and solves for the missing one:
- Find braking acceleration: enter velocity before braking and stopping distance. The calculator uses
a = v² / (2d). - Find stopping distance: enter velocity before braking and braking acceleration. The calculator uses
d = v² / (2a). - Find velocity before braking: enter stopping distance and braking acceleration. The calculator uses
v = √(2ad).
Inputs are converted internally to meters, seconds, and meters per second squared before the result is converted back to your selected unit.
Common Unit Conversions for Braking Calculations
| Quantity | Unit | Base unit conversion |
|---|---|---|
| Velocity | km/h | 1 km/h = 0.277778 m/s |
| Velocity | mph | 1 mph = 0.44704 m/s |
| Velocity | ft/s | 1 ft/s = 0.3048 m/s |
| Distance | ft | 1 ft = 0.3048 m |
| Acceleration | ft/s² | 1 ft/s² = 0.3048 m/s² |
Braking Acceleration Compared With Gravity
Braking acceleration is often compared with standard gravity, where 1 g is about 9.81 m/s².
| Braking acceleration | Approximate g-force | General interpretation |
|---|---|---|
| 2.0 m/s² | 0.20 g | Gentle braking |
| 4.0 m/s² | 0.41 g | Moderate braking |
| 7.0 m/s² | 0.71 g | Hard braking |
| 9.81 m/s² | 1.00 g | Very high deceleration |
Example Calculations
Example 1: Find braking acceleration
You are traveling at 20 m/s and stop in 50 m. Find the braking acceleration.
a = v^2/(2d)
a = 20^2/(2*50) = 400/100 = 4 m/s^2
The braking acceleration is 4 m/s².
Example 2: Find stopping distance
A vehicle is moving at 60 mph and brakes with an acceleration of 6 m/s². First convert 60 mph to meters per second.
60 mph = 60*0.44704 = 26.8224 m/s
d = v^2/(2a)
d = 26.8224^2/(2*6) = 59.94 m
The stopping distance is about 59.94 m.
FAQ
Is braking acceleration negative?
In physics, acceleration during braking is often written as negative because it acts opposite the direction of motion. This calculator uses the magnitude of braking acceleration, so you enter it as a positive value. For example, a deceleration of -4 m/s² is entered as 4 m/s².
Does this include reaction distance?
No. The stopping distance in the formula is the distance traveled while braking under constant deceleration. It does not include the distance traveled during driver reaction time before braking begins.
Why does speed have such a large effect on stopping distance?
Stopping distance is proportional to the square of velocity. If speed doubles and braking acceleration stays the same, the braking distance becomes four times larger.
