# How long is the stopping distance?

Stopping distance calculator: the reaction distance plus the braking distance of a vehicle from its speed, the reaction time and the braking deceleration or road friction, on a level road or a grade.

- Page: https://www.acalculator.org/physics/stopping-distance-calculator
- JSON spec: https://www.acalculator.org/physics/stopping-distance-calculator.json
- Version: 9860bcc7df2a

## Default answer

Example with the default inputs (Speed 60 mph, Reaction time (s) 2.5, Braking by Deceleration rate, Deceleration 11.2, Deceleration unit ft/s², Grade 0%): At 60 mph, the stopping distance is 565.7 ft: 220 ft of reaction and 345.7 ft of braking.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| v | Speed | The speed when the driver sees the hazard. |
| t | Reaction time (s) | The seconds from seeing the hazard to braking: 2.5 s in AASHTO road design. |
| by | Braking by | Give the braking as a deceleration rate or as a tire-road friction coefficient. |
| a | Deceleration | How fast the vehicle slows while braking: 11.2 ft/s² (3.4 m/s²) in AASHTO road design. |
| au | Deceleration unit | The unit of the deceleration you type. |
| mu | Friction coefficient (μ) | Kinetic friction of rubber on the road: about 0.7 on dry concrete and 0.5 on wet concrete. |
| g | Grade | The slope of the road: positive uphill, negative downhill. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| total | Stopping distance | Reaction distance plus braking distance. |
| reactionDistance | Reaction distance | v × t: the distance covered before the brakes go on. |
| brakingDistance | Braking distance | v² ÷ (2 × (a + g × grade)): the distance while braking. |
| totalM | Stopping distance (m) | The stopping distance in metres. |
| totalFt | Stopping distance (ft) | The stopping distance in feet. |
| time | Time to stop (s) | t + v ÷ (a + g × grade). |
| decelUsed | Deceleration used (m/s²) | The braking deceleration plus g × grade, in metres per second squared. |

## Method

Stopping distance = v × t + v² ÷ (2 × (a + g × G)), with v the speed, t the reaction time, a the braking deceleration (or μ × g), G the grade as a decimal (uphill positive) and g = 9.80665 m/s²; time to stop = t + v ÷ (a + g × G).

## Assumptions

- Constant speed during the reaction time and constant deceleration while braking (OpenStax §3.4).
- The grade adds g × G to the deceleration, as in AASHTO’s braking distance on a grade (which uses g = 32.2 ft/s²).

## Worked examples

1. v = 13.4112, t = 2.5, by = rate, a = 11.2, au = fts2, g = 0% gives totalFt = 196.428571, reactionDistance = 33.528, brakingDistance = 26.343429. Source: TxDOT Roadway Design Manual, 4.11.1 Stopping Sight Distance (2.5 s brake reaction time, 11.2 ft/s² deceleration; Table 4-23: 30 mph 110.3 + 86.4 = 196.7 ft, 60 mph 220.5 + 345.5 = 566.0 ft, from AASHTO’s SSD = 1.47Vt + 1.075V² ÷ a), https://www.txdot.gov/manuals/des/rdw/chapter-4--basic-design-criteria/4-11-sight-distance/4-11-1-stopping-sight-distance.html (retrieved 2026-10-18); FHWA, Self-Enforcing Roadways: A Guidance Report (FHWA-HRT-17-098), Chapter 3 (AASHTO 2011: SSD = 1.47Vt + 1.075V² ÷ a, t = 2.5 s; on a grade d = V² ÷ (30((a ÷ 32.2) ± G))), https://www.fhwa.dot.gov/publications/research/safety/17098/004.cfm (retrieved 2026-10-18).
2. v = 26.8224, t = 2.5, by = rate, a = 11.2, au = fts2, g = 0% gives totalFt = 565.714286, time = 10.357143. Source: TxDOT Roadway Design Manual, 4.11.1 Stopping Sight Distance (2.5 s brake reaction time, 11.2 ft/s² deceleration; Table 4-23: 30 mph 110.3 + 86.4 = 196.7 ft, 60 mph 220.5 + 345.5 = 566.0 ft, from AASHTO’s SSD = 1.47Vt + 1.075V² ÷ a), https://www.txdot.gov/manuals/des/rdw/chapter-4--basic-design-criteria/4-11-sight-distance/4-11-1-stopping-sight-distance.html (retrieved 2026-10-18).
3. v = 30, t = 0.5, by = rate, a = 7, au = ms2, g = 0% gives total = 79.285714, reactionDistance = 15, brakingDistance = 64.285714. Source: OpenStax, University Physics Volume 1, §3.4 Motion with Constant Acceleration (Equation 3.14, v² = v₀² + 2a(x − x₀); Example 3.10: 30.0 m/s, 0.500 s, 7.00 m/s² dry or 5.00 m/s² wet: 79.3 m or 105 m), https://openstax.org/books/university-physics-volume-1/pages/3-4-motion-with-constant-acceleration (retrieved 2026-10-18): 15.0 m + 64.3 m = 79.3 m.
4. v = 30, t = 0.5, by = rate, a = 5, au = ms2, g = 0% gives total = 105, brakingDistance = 90. Source: OpenStax, University Physics Volume 1, §3.4 Motion with Constant Acceleration (Equation 3.14, v² = v₀² + 2a(x − x₀); Example 3.10: 30.0 m/s, 0.500 s, 7.00 m/s² dry or 5.00 m/s² wet: 79.3 m or 105 m), https://openstax.org/books/university-physics-volume-1/pages/3-4-motion-with-constant-acceleration (retrieved 2026-10-18): 15.0 m + 90.0 m = 105 m.
5. v = 27.777778, t = 1.5, by = friction, mu = 0.7, g = 0% gives total = 97.867957, decelUsed = 6.864655.
6. v = 26.8224, t = 2.5, by = rate, a = 11.2, au = fts2, g = -3% gives brakingDistance = 115.311298, decelUsed = 3.119561. Source: FHWA, Self-Enforcing Roadways: A Guidance Report (FHWA-HRT-17-098), Chapter 3 (AASHTO 2011: SSD = 1.47Vt + 1.075V² ÷ a, t = 2.5 s; on a grade d = V² ÷ (30((a ÷ 32.2) ± G))), https://www.fhwa.dot.gov/publications/research/safety/17098/004.cfm (retrieved 2026-10-18).

## FAQ

### How do you calculate stopping distance?

Add the reaction distance to the braking distance: d = v × t + v² ÷ (2a). At 30.0 m/s with a 0.500 s reaction and 7.00 m/s² of braking, the car travels 15.0 m while reacting and 900 ÷ 14 = 64.3 m while braking: 79.3 m in all.

### What is the stopping distance at 60 mph?

With the AASHTO design values (2.5 s reaction, 11.2 ft/s² braking), 60 mph (88 ft/s) gives 88 × 2.5 = 220 ft of reaction and 88² ÷ 22.4 = 345.7 ft of braking: 565.7 ft. Highway designers round this up to 570 ft.

### Why does doubling the speed more than double the stopping distance?

The braking distance grows with the square of the speed. Twice the speed gives twice the reaction distance but four times the braking distance.

### What reaction time should I use?

AASHTO uses 2.5 s for road design. OpenStax uses 0.5 s in its example of a driver ready to brake.

### How does a wet road change the stopping distance?

A wet road brakes less hard. OpenStax gives about 7 m/s² on dry concrete and 5 m/s² on wet concrete: from 30 m/s the braking distance grows from 64.3 m to 90.0 m. With friction, use μ = 0.7 dry and 0.5 wet.

### How does a hill change the stopping distance?

Going uphill, gravity helps the brakes; going downhill, it works against them. The page adds g × grade to the deceleration: a 3% downhill grade takes 0.294 m/s² away from the braking.

## Sources

- OpenStax, University Physics Volume 1, §3.4 Motion with Constant Acceleration: Equation 3.14, v² = v₀² + 2a(x − x₀); Example 3.10, How Far Does a Car Go? (30.0 m/s, 0.500 s, 7.00 or 5.00 m/s²: 79.3 m or 105 m), retrieved 2026-10-18. https://openstax.org/books/university-physics-volume-1/pages/3-4-motion-with-constant-acceleration
- FHWA, Self-Enforcing Roadways: A Guidance Report (FHWA-HRT-17-098), Chapter 3: AASHTO 2011 stopping sight distance SSD = 1.47Vt + 1.075V² ÷ a with t = 2.5 s, and braking distance on a grade V² ÷ (30((a ÷ 32.2) ± G)), retrieved 2026-10-18. https://www.fhwa.dot.gov/publications/research/safety/17098/004.cfm
- Texas Department of Transportation, Roadway Design Manual, 4.11.1 Stopping Sight Distance: 2.5 s brake reaction time, 11.2 ft/s² deceleration; Table 4-23, retrieved 2026-10-18. https://www.txdot.gov/manuals/des/rdw/chapter-4--basic-design-criteria/4-11-sight-distance/4-11-1-stopping-sight-distance.html
- OpenStax, College Physics 2e, §5.1 Friction: Table 5.1, rubber on dry concrete μk = 0.7, on wet concrete μk = 0.5, retrieved 2026-10-18. https://openstax.org/books/college-physics-2e/pages/5-1-friction
- NIST, CODATA 2022: standard acceleration of gravity g = 9.80665 m/s² (exact), retrieved 2026-10-18. https://physics.nist.gov/cgi-bin/cuu/Value?gn
- NIST Special Publication 811 (2008), Appendix B.8: 1 mph = 0.44704 m/s, 1 ft = 0.3048 m, retrieved 2026-10-18. https://www.nist.gov/pml/special-publication-811