Slider Crank Kinematics Calculator
Calculate ideal piston displacement from top dead center and signed velocity/acceleration at constant crank 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
Differentiate exact rigid-link displacement with respect to crank angle and apply constant angular speed.
Travel from TDC=r+l−r cosθ−sqrt(l²−r²sin²θ)
Worked example
Travel is zero at0°, twice crank radius at180°, and generally exceeds crank radius at90° with a finite rod.
Assumptions and input details
Rod length must exceed crank radius; offset-free rigid mechanism and constant crank speed. No combustion, bearing force, deformation, acceleration of the input shaft or engine rating.
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.
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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