Velocity & Acceleration Calculator

This calculator solves the standard constant-acceleration kinematics equations for whichever quantity you designate as unknown -- final velocity, acceleration, time, or distance -- using the other three as known inputs. Solve For fundamentally changes which equation runs: choosing Time, for instance, switches to the quadratic form and solves it via the quadratic formula rather than simple algebra, and that mode-switch means Result itself represents a different physical quantity depending on the selection, so its formula and even its unit change with the mode. Final Velocity and Displacement, by contrast, are computed consistently across every mode using the same underlying physics: Final Velocity always equals initial velocity plus the applicable acceleration times time -- using the value you entered in Acceleration when it's a known input, or the freshly solved acceleration when Solve For is set to Acceleration itself, since the raw Acceleration field isn't meaningful data in that one mode. Displacement always tracks either the entered Distance value directly or the same v0*t + half*a*t-squared formula, depending on which mode is active.

Negative Acceleration models deceleration or braking rather than requiring a separate input -- entering a negative value there is the standard way to represent slowing down in these equations, not an error condition. When Solve For is set to Time and the object decelerates to rest before covering the entered Distance, no real solution exists -- the calculator reports Distance Reachable as No and shows the furthest point actually reached as Displacement rather than returning a spurious zero time. Displacement is also a signed position change, not a distance travelled: with a negative Initial Velocity and a positive Acceleration the object first moves backwards, reaches its most negative displacement at t = -v0/a, and only then returns through the origin -- entering v0 = -100 m/s with a = 9.81 m/s2, for example, gives -509.5 m at 10 s and +7,262.5 m at 50 s.