Choose braking deceleration, braking distance, or speed before braking, then enter the two displayed inputs. Speed supports m/s, km/h, mph, and ft/s; distance and deceleration have their own units.

Assumes constant deceleration to a complete stop. Braking distance excludes reaction distance. Enter deceleration as a positive magnitude.

Use speed as a nonnegative magnitude. Changing units converts the value.

Distance from the start of braking to a complete stop; excludes reaction distance.

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 = v² / (2d)
d = v² / (2a)
v = sqrt(2ad)
  • a = braking acceleration, usually treated as a positive deceleration value
  • v = velocity before braking
  • d = braking distance, excluding reaction distance

Select the value to solve for and enter the other two values:

  • 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 Magnitude comparison
2.0 m/s² 0.20 g About one fifth of standard gravity
4.0 m/s² 0.41 g About two fifths of standard gravity
7.0 m/s² 0.71 g About seven tenths of standard gravity
9.81 m/s² 1.00 g About standard gravity

Example Calculations

Example 1: Find braking acceleration

You are traveling at 20 m/s and stop in 50 m. Find the braking acceleration.

a = v² / (2d)
a = 20² / (2 × 50) = 400 / 100 = 4 m / s²

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 = v² / (2a)
d = 26.8224² / (2 × 6) ≈ 59.95 m

The stopping distance is about 59.95 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.