Centripetal Acceleration Calculator
The centripetal acceleration calculator works out how fast anything moving in a circle is accelerating toward the centre. Enter any two of the four values — radius, tangential velocity, angular velocity, or period — and it instantly returns the centripetal acceleration in m/s² and its g-force equivalent, then auto-fills the two variables you left blank. Every unit has its own dropdown (metres or feet, m/s or mph, rad/s or RPM, seconds or minutes), and everything is solved right in your browser — no signup, nothing uploaded.
Type any two of the four fields — radius, tangential velocity, angular velocity, or period — and the centripetal acceleration in m/s² and g-force appears at the top, while the other two fields fill in automatically. Each field has its own unit dropdown, and the Units & precision panel lets you switch between Metric and Imperial, rad/s and RPM, and the number of decimals.
Know any two of radius, velocity, angular velocity, or period? Get the acceleration in one look.
Use the free Centripetal Acceleration Calculator →How to Use the Centripetal Acceleration Calculator
Circular motion has four linked quantities, and knowing any two fixes the rest — so there is no fixed "input box" you must use. Type the two you know and read the answer; the result updates the moment you type, with no submit button:
- Open capsuletools.app/centripetal-acceleration/
- Type any two values — for example a radius and a velocity, or a radius and an angular velocity, or a radius and a period
- Pick the units for each field from its dropdown (metres, feet, mph, RPM, seconds, and so on)
- Read the result — the big number is the centripetal acceleration, with the g-force shown just below; the two fields you left blank fill in automatically in a muted colour
- Open Units & precision to switch the whole calculator between Metric and Imperial, choose rad/s or RPM, or change the number of significant figures
Because the tool solves the whole system, you can also use it as a plain converter — enter a radius and an RPM and it hands you the linear velocity and period alongside the acceleration.
Velocity = 20 m/s
Centripetal acceleration = 8 m/s²
G-force = 0.82 g
Centripetal Acceleration Formulas
Centripetal acceleration always points toward the centre of the circle. Which formula the calculator uses depends on which two values you enter, but they all describe the same quantity:
| You know | Formula used |
|---|---|
| Radius & velocity | a = v² / r |
| Radius & angular velocity | a = ω²r |
| Velocity & angular velocity | a = vω |
| Radius & period | a = 4π²r / T² |
These are tied together by two simple relationships: linear velocity is v = ωr, and the angular velocity and period are linked by ω = 2π / T. That is also why angular velocity and period on their own can't give an acceleration — they describe the same rotation and carry no size, so the calculator asks for a radius or a velocity as well.
Reading Your Results: m/s² and G-Force
The main result is the acceleration in metres per second squared (or feet per second squared in Imperial mode). Directly beneath it is the same figure expressed as a g-force — a multiple of standard gravity, 9.80665 m/s²:
So 8 m/s² is about 0.82 g, and 20 m/s² is roughly 2 g. G-force is the intuitive way to feel a result: 1 g is your normal body weight, a hard cornering car reaches about 1 g, a jet fighter pulls up to 9 g, and a lab centrifuge can hit thousands of g. Showing both units lets you check homework in SI and still picture what the number means.
Real-World Examples
The same four-variable solver covers everything from a playground to low Earth orbit:
- Car on a curve — 50 m radius at 20 m/s → a = 20² / 50 = 8 m/s² (0.82 g)
- Vinyl record — 33.3 RPM, 0.15 m from the spindle → a ≈ 1.8 m/s² (0.19 g)
- Lab centrifuge — 5000 RPM, 0.1 m rotor → a ≈ 27,400 m/s² (about 2800 g)
- ISS in orbit — radius 6.771×10⁶ m, period 5580 s → a ≈ 8.6 m/s² (0.88 g)
Enter any of these pairs into the calculator and it reproduces the acceleration and fills in the remaining variables — the orbital speed of the ISS comes out at about 7.6 km/s, for instance.
Frequently asked questions
How do you calculate centripetal acceleration from RPM?
First convert RPM to angular velocity in radians per second: ω = RPM × 2π ÷ 60. Then centripetal acceleration is a = ω²r, where r is the radius. For example, a turntable spinning at 33.3 RPM has ω = 33.3 × 2π ÷ 60 ≈ 3.49 rad/s, so a point 0.15 m from the centre feels a = 3.49² × 0.15 ≈ 1.83 m/s². In this calculator you just switch the angular-velocity unit to RPM, type the RPM and the radius, and the acceleration appears instantly.
How do you calculate centripetal acceleration from angular velocity?
When you know the angular velocity ω (in radians per second) and the radius r, centripetal acceleration is a = ω²r. There is no need to find the linear velocity first. For instance, ω = 4 rad/s at r = 2 m gives a = 4² × 2 = 32 m/s². Enter the angular velocity and the radius in the calculator and it applies a = ω²r for you, and also fills in the matching linear velocity and period.
How do you find centripetal acceleration using the period of rotation?
The period T is the time for one full revolution, and it relates to acceleration through a = 4π²r ÷ T². So a wheel of radius 0.3 m turning once every 2 seconds has a = 4π² × 0.3 ÷ 2² = 4π² × 0.3 ÷ 4 ≈ 2.96 m/s². Type the radius and the period into the calculator and it uses this formula automatically — no need to work out the angular velocity yourself.
Can you calculate centripetal acceleration without knowing the velocity?
Yes. Centripetal acceleration only needs any two independent quantities out of radius, tangential velocity, angular velocity, and period. Without velocity you can use radius plus angular velocity (a = ω²r) or radius plus period (a = 4π²r ÷ T²). This calculator is built around that idea: type any two of the four values and it solves for the acceleration and auto-fills the two you left blank, including the velocity.
What is centripetal acceleration in units of g?
Expressing acceleration in g means comparing it to standard gravity, 9.80665 m/s². Divide the acceleration by that number: an acceleration of 8 m/s² is 8 ÷ 9.80665 ≈ 0.82 g. Fighter pilots, roller coasters, and centrifuges are often described this way because g-force is intuitive — 1 g feels like your own body weight. This calculator shows both m/s² and the g-force equivalent for every result.
How do you convert RPM to g-force for a centrifuge?
Convert the spin speed to angular velocity (ω = RPM × 2π ÷ 60), compute the acceleration with a = ω²r, then divide by 9.80665 m/s² to get g. A rotor spinning at 5000 RPM with a 0.1 m radius gives ω ≈ 523.6 rad/s, a ≈ 27,400 m/s², or about 2800 g — this is the same quantity a lab calls relative centrifugal force (RCF). Set the angular unit to RPM in the calculator, enter the RPM and radius, and read the g-force straight off.
How do you find the centripetal acceleration of a satellite in orbit?
A satellite in a circular orbit is in uniform circular motion, so its centripetal acceleration comes from its orbital radius and period: a = 4π²r ÷ T². The International Space Station orbits at a radius of about 6.771 million metres with a period near 5580 seconds, giving a ≈ 8.59 m/s² — roughly 0.88 g, which is why astronauts still feel almost full gravity but appear weightless because they are in free fall. Enter the orbital radius and the period and the calculator returns the acceleration and the orbital speed.
Use the free Centripetal Acceleration Calculator →
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