DIY Cost Tools
Centripetal Force Calculator
Calculate inward force, centripetal acceleration, and angular speed from mass, speed, and circular path radius. Start with the prefilled example or enter your measurements in SI units.
Mass and radius must be positive. Speed must be nonnegative; zero gives zero results. All fields are required. Numeric magnitude is limited to 1 trillion.
How to use
Convert inputs to the units printed on each field, enter a value in every box, and select Calculate. Default results appear on page load. Invalid entries clear old results and show an explanation. Answers display up to ten significant digits; measurement uncertainty and floating-point rounding affect precision.
Formula and explanation
F = mv²/r; a = v²/r; ω = v/r. Mass m is in kilograms, tangential speed v in metres per second, and radius r in metres. The force points toward the center. It describes the inward net force, which can come from tension, gravity, friction, or several forces together.
Worked example
A 2 kg object traveling at 6 m/s around a 3 m radius needs 24 N inward force, with 12 m/s² centripetal acceleration and 2 rad/s angular speed.
Limitations and safety
Assumes classical motion along a circular path. For changing speed, this computes the radial component only; tangential acceleration is separate. It does not calculate friction capacity, banking, braking distance, safe driving speed, or equipment strength. Do not use it to establish vehicle or machinery safety limits.
Frequently asked questions
Why is force proportional to speed squared?
Doubling speed while holding mass and radius fixed makes the required inward acceleration and force four times larger.
Is centripetal force an extra force?
It names the net inward force responsible for curved motion, rather than an additional interaction.
Can I enter km/h?
Convert km/h to m/s by dividing by 3.6 before entering speed.
Does a larger radius increase force?
At fixed speed and mass, a larger radius reduces required force.
Review notes
Reviewed October 1, 2026. Formulas checked against OpenStax University Physics. Default results and boundary cases were independently tested, along with blank, nonfinite, excessive, and invalid inputs. This calculator is an educational estimate, not an engineering safety assessment.