Example 1
Car at 14 m/s on a 40 m arc.
Centripetal Acceleration Calculator
Type v [m/s] and r [m]. The calculator computes a = v²/r: 14 m/s on a 40 m arc is 4.9 m/s², and 10 m/s and r = 35 m is about 2.86 m/s². A zero-metre radius does not divide.
Force from this a: F = m·v²/r. Straight line: a = Δv/t. v from ω: v = ω·r.
Result
Speed v (m/s) and Radius r (m). The result shows up here.
How it works
Centripetal acceleration says how fast velocity changes direction on a circle: a = v² / r. At 14 m/s and r = 40 m you get 196 / 40 = 4.9 m/s². At 10 m/s and r = 35 m you get 100 / 35 ≈ 2.86 m/s². Direction of a is toward the center; the value is non-negative.
The form has two fields: v in m/s and r in meters. The result is in m/s². v is squared, so 20 m/s on the same 40 m would be 10 m/s², not 9.8. A comma and a period are the same v: 14,5 and 14.5.
r must be positive. Zero meters does not divide: no circle, no a. Typed 0 in v gives a = 0, because speed does not change direction when it is standing still. Both fields need a number before 4.9 m/s² can appear.
In a straight line you use a = Δv/t. At constant |v| the scalar Δv is zero, but direction changes, and that is what a = v²/r describes. Force from this a is on the neighbouring page: F = m v²/r.
v from ω is on v = ω r. From 10 rad/s and 0.35 m you have 3.5 m/s; bring that here with the same r and you get 35 m/s².
Type 14 and 40, click Calculate, and match 4.9 m/s². The header symbol does not bend the path. Treat the result as the inward magnitude, not as a straight-line acceleration.
How to use
- In the first field enter v in m/s. For example 14. That is tangential speed, not angular.
- In the second field enter r in meters, for example 40. Zero will not run, because you divide by r.
- Click Calculate. The calculator computes v²/r. 14 m/s and 40 m give 4.9 m/s².
- Typed 0 in v gives a = 0. r must be greater than zero. Both fields need a number.
- For force F = m a, open centripetal force. v from ω lives on v = ω r.
Formula
a = v2 / r
v is linear (tangential) speed, r is the circle radius. The result a is centripetal acceleration toward the center.
a, v, and r for centripetal acceleration
Just a = v²/r, no mass. 14 m/s and 40 m is 4.9 m/s². 20 m/s on the same 40 m would be 10 m/s², not 9.8.
- a
- Inward acceleration [m/s²]. 196 / 40 = 4.9. Not g from the free-fall calculator.
- v
- Tangential linear speed [m/s]. 14 m/s. Squared in the numerator.
- r
- Circle radius [m]. 40 m. Positive. Force F = m a is on another calculator.
Real-life examples
Example 2
28 m/s (about 100 km/h) with r = 120 m.
Example 3
Seat at 6 m moving 8 m/s.
Example 4
8 m/s on r = 15 m.
Example 5
Sample at 0.10 m with 30 m/s.
Example 6
v ≈ 7800 m/s, r ≈ 6771000 m (Earth + 400 km).
Example 7
Whirling a stone: v = 5 m/s, r = 1.2 m.
Example 8
Skater 12 m/s on a 25 m arc.
Example 9
At the bottom: v = 20 m/s, r = 10 m.
Example 10
10 m/s and r = 35 m.
Ways to use this calculator
- You compute 4.9 m/s² from 14 m/s on a 40 m arc.
- You compare with a = Δv/t, which does not describe a turn at constant |v|.
Frequently asked questions
How much a at 14 m/s and r = 40 m?
Acceleration is 4.9 m/s². 14 squared is 196, over 40. That is not g from the free-fall calculator, even when the number is close.
Which units do I type?
Speed v [m/s], radius r [m]. Result a [m/s²]. 50 km/h is about 13.9 m/s, not 50 in field v.
What if v = 0?
Acceleration is 0 m/s². You are standing still, so v² vanishes. r must still be positive before the calculator divides.
Where is F = m v²/r?
On the centripetal-force page. There you multiply this a by mass. Here only a = v²/r, with no m.
How is this different from a = Δv/t?
Here a points to the centre of the circle, from speed and radius. There you have average acceleration from a change in v over time, on a line.
Can a be negative?
In this model a is the inward magnitude, not negative. The direction still points to the centre of the arc, not the rear of the car.
Does a comma in 14.5 work?
Yes. 14.5 and 14,5 are the same v [m/s]. A comma and a period mean the same value.
Why is v squared?
Twice as fast on the same r gives four times a. 20 m/s on 40 m is 10 m/s², not 9.8.
Where do I get v if I know ω?
From the v = ω r card. This field already wants metres per second, not radians per second.
What if r is very small?
a grows. The same v on a tight arc gives a large acceleration. r = 0 is rejected, because you do not divide by zero.
Knowledge sources
The formula is the school one. Units follow SI; NIST SP 330 and BIPM define the measures, not your result.
Page updated in 2026.