THE NUMORIX GUIDE
How to use the Free Fall Calculator
Last reviewed September 14, 2026
What this calculator does
The engine solves h = v_0t + 1/2gt^2 for the nonnegative impact time: t = (-v_0 + sqrt(v_0^2 + 2gh)) / g.
Formula and method
The engine solves h = v_0t + 1/2gt^2 for the nonnegative impact time: t = (-v_0 + sqrt(v_0^2 + 2gh)) / g. It then calculates impact velocity with v = v_0 + gt.
Variables and inputs
Height h is in meters, initial velocity v_0 in m/s, and gravitational acceleration g in m/s^2. The default is h = 20 m, v_0 = 0, and g = 9.81; height cannot be negative and gravity must be positive.
Worked example
For h = 20 m, v_0 = 0, and g = 9.81 m/s^2: t = sqrt(2(20)/9.81) = 2.0193 s, then impact velocity = 0 + 9.81(2.0193) = 19.8091 m/s.
How to interpret the result
The result is the positive time to reach the lower reference level under constant downward acceleration. A positive initial velocity is treated as downward in the engine's equation; a negative value represents an initial upward component in that sign convention.
Common mistakes to avoid
Use height in meters and do not use g = 9.81 as a mass or force. Keep the sign of initial velocity consistent with the chosen downward direction, and do not assume a dropped object has zero air resistance in reality.
Assumptions and limitations
This is an ideal constant-gravity model with no air resistance, wind, rotation, buoyancy, or changing gravitational field. It does not check whether a real object would reach the stated height or survive impact; the zero-height case returns zero time and the entered initial velocity.
Practical use and checks
The Free Fall Calculator estimates time and impact speed for an object dropped or launched vertically under constant gravity. Enter height 20 m, initial velocity 0 m/s, and gravity 9.81 m/s^2 as a check; time should be about 2.0193 seconds and impact speed about 19.8091 m/s. With a nonzero initial downward velocity, the result changes because the calculator includes that term rather than using only square root of 2h/g. Keep the sign convention clear when entering an upward launch. Use height as vertical distance to the chosen landing level, not as a path length, and use gravity in m/s^2. A negative initial velocity can represent upward motion under the engine's convention, while the positive solution is the selected impact time. The model assumes constant gravity and no air resistance, wind, drag, buoyancy, rotation, or obstacles. A light object, a high drop, or a parachute will depart from the ideal result, and the calculator does not decide whether the object reaches the stated height or survives impact. Zero height is an edge case that can return zero time and the entered initial velocity. For a real safety or timing decision, include drag, release height, terrain, and measurement uncertainty instead of treating the ideal impact speed as a prediction.