Centripetal Force Calculator
Calculate the inward net force, acceleration, angular speed and period for uniform circular motion from mass, radius and linear or angular speed.
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Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Convert the selected speed and radius to SI. Use v=ωr to relate linear and angular motion, then apply inward acceleration v²/r and Newton’s second law to the net radial force.
a_c=v²/r=ω²r; F_c=ma_c
Worked example
A 2 kg mass moving at 3 m/s on a 0.5 m radius path has centripetal acceleration 18 m/s² and needs 36 N of inward net force.
Assumptions and input details
Uniform circular motion with positive radius and nonnegative speed magnitude. The result is the required inward net force, not a new physical force type; tension, gravity, friction or another real interaction must supply it. Direction, banking, safety factors, component strength, drag and changing speed are excluded. At zero speed the force is zero and the revolution period is not finite.
References: NASA Imagine the Universe: uniform circular motion
Unit definitions
Unit selection is independent of language. Each selector contains only units for its physical quantity. Calculations use defined base units internally.
Choose from 23 length definitions, including explicitly labelled regional measures. Area conversions square the length factor; geometric volumes cube it.
The 19 mass definitions distinguish avoirdupois and troy measures, metric and regional measures. Japanese kin is 600 g; mainland Chinese shijin is 500 g.
Regional measures are not interchangeable merely because their names look similar. This is a documented selection, not a claim to include every historical unit.
One revolution is 2π radians or 360 degrees. One minute is 60 seconds, so 1 rpm = 2π/60 rad/s. Rotational frequency in hertz counts revolutions per second.
NIST measurement tables · Japanese traditional units · Mainland China and Hong Kong unit distinctions
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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