What is the centripetal force formula?

The centripetal force is F = m·v²/r, where m is mass in kilograms, v is tangential speed in metres per second and r is the radius in metres, giving force in newtons. For example a 2 kg ball swung at 3 m/s on a 1 m string needs F = 2 × 9 / 1 = 18 N pulling inward. The same relation can be written F = m·ω²·r when you know the angular speed ω in rad/s, since v = ω·r.

What is centripetal acceleration and how is it different from the force?

Centripetal acceleration is a = v²/r, measured in metres per second squared, and it is the rate at which the velocity direction changes as the object turns. The force is just mass times that acceleration: F = m·a. For a car taking a 50 m bend at 20 m/s, a = 400 / 50 = 8 m/s²; multiply by the 1200 kg mass and the tyres must supply 9600 N of grip toward the centre.

Why does doubling the speed multiply the force by four?

Because the speed appears squared in F = m·v²/r. If you keep the same mass and radius but double v, the v² term becomes four times larger, so the force is four times larger. This is why a car going twice as fast around the same corner needs four times the friction, and why cornering speed has such an outsized effect on whether the tyres can hold the road.

How do I use angular velocity ω instead of linear speed?

Switch the speed field to angular mode and enter ω in radians per second. The tool computes the tangential speed v = ω·r and then the force, which is equivalent to F = m·ω²·r. For example a 0.5 kg mass on a 2 m arm spinning at ω = 4 rad/s has v = 8 m/s, so F = 0.5 × 64 / 2 = 16 N. One full turn per second is ω = 2π ≈ 6.283 rad/s.

What is the difference between centripetal and centrifugal force?

Centripetal force is a real inward force (tension, gravity, friction or normal force) that bends the path into a circle and points toward the centre. Centrifugal force is the apparent outward push you feel in a rotating frame; it is not a separate force acting on the object but the body's inertia trying to go straight. This calculator gives the genuine centripetal force, so its direction is always toward the centre, not away from it.

Can I solve for the radius or the speed instead of the force?

Yes. Pick the solve mode for mass, speed or radius and the tool rearranges the formula: m = F·r/v², v = √(F·r/m), or r = m·v²/F. For instance, if a 0.2 kg stone needs 5 N of centripetal force at 4 m/s, the radius is r = 0.2 × 16 / 5 = 0.64 m. Reverse solving is handy for lab questions that give you the force and ask for the geometry.

Check circular-motion homework before you hand it in

Your problem set gives a 0.15 kg ball on a 0.8 m string whirling at 5 m/s and asks for the tension. Type the three values, read 4.69 N, and compare it with the answer you worked by hand. If they disagree, the formula steps on screen show exactly where your arithmetic diverged, so you fix the slip instead of guessing which line was wrong.

Set up a conical-pendulum or banked-curve lab

Planning a lab where students measure the force needed to keep a mass on a turntable? Pick a target speed and radius, read the required centripetal force, and size the spring scale or string accordingly so nothing snaps mid-demo. Switch to angular mode to enter the turntable's ω directly in rad/s instead of converting RPM by hand.

Estimate the cornering grip a vehicle needs

A 1300 kg car takes a 40 m bend at 18 m/s. Enter mass, speed and radius to get the centripetal force the tyres must supply toward the centre, then compare it against the available friction (μ·m·g) to see whether the corner is safe at that speed. Halving the radius or raising the speed shows instantly how the demand climbs.

Size a rotating part for a maker or robotics build

A 0.3 kg weight sits at the 0.25 m rim of a spinning arm running at ω = 12 rad/s. Use angular mode to find the inward force the joint and fasteners must hold, so you choose a bolt and bracket that will not let go at speed. Reverse-solve for the maximum safe speed given the fastener's rated load.

Sanity-check an amusement-ride or satellite figure

Reading that a rotor ride spins guests at 2.5 m radius and pins them with about 3 g of acceleration? Put 2.5 m and the speed in, confirm the acceleration, and the centripetal force per kilogram follows. The same setup checks a satellite's required inward force from its orbital speed and radius.

Centripetal Force Calculator: F = m·v²/r

Solve F = m·v²/r for force, mass, speed or radius, with angular speed ω and centripetal acceleration, browser-only

Runs locally
Category Calculator
Best for Getting a realistic range before a purchase, plan, workout, or schedule decision.

What do you want to solve for?

Mass m

Speed

Radius r

Centripetal force F

Result

Centripetal force18 N

Centripetal acceleration a = v²/r9 m/s²

The force points toward the centre of the circle.

Formula steps

F = m·v²/r
F = 2 kg × (3 m/s)² / 1 m
F = 2 × 9 / 1
F = 18 N
a = v²/r = (3 m/s)² / 1 m = 9 m/s²

What this tool does

A free centripetal force calculator for circular motion homework, lab reports and engineering checks. Centripetal force is the inward force that keeps an object on a circular path: F = m·v²/r, where m is mass in kilograms, v is tangential speed in metres per second and r is the radius in metres. Enter any three of mass, speed and radius to get the force in newtons, or switch the solve mode to reverse the formula and find the mass, the speed or the radius from a known force. Prefer to think in revolutions? Toggle the speed field to angular velocity ω in rad/s and the tool computes v = ω·r first, then the same force. Every result also shows the centripetal acceleration a = v²/r, the formula steps so you can copy the working into a report, and a one-click copy button. The result is the magnitude; the direction always points toward the centre of the circle. Everything runs in your browser and the share link reproduces the exact problem. 100% client-side, no upload.

Tool details

Input: Files + Numbers; The page exposes text boxes, numeric controls, file pickers, or structured inputs depending on the tool.
Output: Live result + Copy; The result area focuses on usable output, with copy, download, or preview actions when supported.
Privacy: Browser-side processing; The main tool logic does not call an external API, so inputs normally stay in the current tab.
Save / share: Shareable URL state; Key settings are encoded in the URL so another person can reopen the same setup.
Performance budget: Initial JS <= 9 KB; No WASM budget is declared, keeping the tool quick to open on mobile.
Best fit: Calculator · Student; Category and role tags drive related tools, internal links, and quick fit checks.

How to use

1. Input

Paste or drop your content into the tool panel.
2. Process

Click the button. All processing is local in your browser.
3. Copy / Download

Copy the result or download to disk in one click.

How Centripetal Force Calculator fits into your work

Use it for fast estimates, comparisons, and planning numbers before you make the final call.

Calculation jobs

Getting a realistic range before a purchase, plan, workout, or schedule decision.
Comparing scenarios by changing one input at a time.
Turning rough assumptions into a number you can discuss.

Calculation checks

Double-check units, dates, rates, and rounding assumptions.
Treat health, finance, tax, and legal outputs as planning aids, not professional advice.
Save the inputs that produced an important result so you can reproduce it later.

Good next steps

These links move the current task into a more complete workflow.

Real-world use cases

Check circular-motion homework before you hand it in
Your problem set gives a 0.15 kg ball on a 0.8 m string whirling at 5 m/s and asks for the tension. Type the three values, read 4.69 N, and compare it with the answer you worked by hand. If they disagree, the formula steps on screen show exactly where your arithmetic diverged, so you fix the slip instead of guessing which line was wrong.
Set up a conical-pendulum or banked-curve lab
Planning a lab where students measure the force needed to keep a mass on a turntable? Pick a target speed and radius, read the required centripetal force, and size the spring scale or string accordingly so nothing snaps mid-demo. Switch to angular mode to enter the turntable's ω directly in rad/s instead of converting RPM by hand.
Estimate the cornering grip a vehicle needs
A 1300 kg car takes a 40 m bend at 18 m/s. Enter mass, speed and radius to get the centripetal force the tyres must supply toward the centre, then compare it against the available friction (μ·m·g) to see whether the corner is safe at that speed. Halving the radius or raising the speed shows instantly how the demand climbs.
Size a rotating part for a maker or robotics build
A 0.3 kg weight sits at the 0.25 m rim of a spinning arm running at ω = 12 rad/s. Use angular mode to find the inward force the joint and fasteners must hold, so you choose a bolt and bracket that will not let go at speed. Reverse-solve for the maximum safe speed given the fastener's rated load.
Sanity-check an amusement-ride or satellite figure
Reading that a rotor ride spins guests at 2.5 m radius and pins them with about 3 g of acceleration? Put 2.5 m and the speed in, confirm the acceleration, and the centripetal force per kilogram follows. The same setup checks a satellite's required inward force from its orbital speed and radius.

Common pitfalls

Plugging in the diameter instead of the radius. The formula uses the radius, the distance from the centre to the object. If you measure the full circle width, halve it first, or the force comes out exactly twice too small.
Forgetting that speed is squared. Centripetal force scales with v², not v, so doubling the speed quadruples the force. Estimating it as linear in speed badly underpredicts cornering and rotor loads.
Mixing centripetal with centrifugal. The real force in this calculator points toward the centre. The outward "centrifugal" feeling is inertia in a rotating frame, not a force on the object, so never enter it as an outward force.
Using RPM where the angular field expects rad/s. Angular speed ω must be in radians per second. To convert, multiply revolutions per second by 2π (or RPM by 2π/60) before entering it.

Privacy

Every calculation, the centripetal-force formula, the reverse solves for mass, speed and radius, the angular-to-linear step and the acceleration, is plain JavaScript running in your browser tab. No numbers you enter ever leave the page and nothing is logged. The one caveat: the shareable URL encodes your inputs in the query string, so a "share link" pasted into chat will record those values in the recipient server's access log. For a private assignment or design figure, use the copy button and paste the text rather than sharing the URL.

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Centripetal Force Calculator: F = m·v²/r

Result

Formula steps

What this tool does

Tool details

How to use

1. Input

2. Process

3. Copy / Download

How Centripetal Force Calculator fits into your work

Calculation jobs

Calculation checks

Good next steps

Real-world use cases

Check circular-motion homework before you hand it in

Set up a conical-pendulum or banked-curve lab

Estimate the cornering grip a vehicle needs

Size a rotating part for a maker or robotics build

Sanity-check an amusement-ride or satellite figure

Common pitfalls

Privacy

FAQ

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