Velocity
Vertical velocity, positive downward.
Physics · Mechanics · Motion & Energy
Free fall calculator
Calculate vertical velocity and displacement after a time, or the fall time from a height when released from rest. The positive axis points downward.
Created v1.0
By Thibaut Grzelak, Mechanical Analysis Engineer
02
Results
Signed displacement
Vertical displacement from release, positive downward.
Elapsed time
Nonnegative elapsed time for this motion.
Relation and numerical substitution
v = v₀ + g × t—
Downward-positive axis; g > 0; no drag. Height mode assumes v₀ = 0.
01Formulas and symbols
Formulas used
v
v = v₀ + g × tVertical velocity, positive downward.Δy
Δy = v₀ × t + ½ × g × t²Vertical displacement from release, positive downward.t
t = √(2 × Δy / g)Nonnegative elapsed time for this motion.v
v = g × tVertical velocity, positive downward.02Assumptions and limits
Scope of validity
- Downward-positive axis; g > 0; no drag. Height mode assumes v₀ = 0.
03Validation example
Reference numerical case
- Released from rest for t = 2 s with g = 9.80665 m/s²: v = gt = 19.6133 m/s; Δy = ½gt² = 19.6133 m. The height mode returns t = 2 s.
04References
Technical references
FAQ
Does mass affect free-fall time?
Not in the ideal no-drag model. All bodies at the same location have the same gravitational acceleration, so mass cancels from the equations of motion.
Why does the sign of gravity depend on the coordinate convention?
Gravity points downward, but the numerical sign depends on which direction you define as positive. If upward is positive, gravitational acceleration is negative; if downward is positive, it is positive.
05How it works
With the downward-positive convention, acceleration is +g. A downward initial velocity is positive and an upward launch is negative. The height mode always starts from rest and returns the positive time to descend the supplied height.
06Limits of the model
Uniform gravity and negligible air resistance. The time mode continues the ideal trajectory; it does not detect collision with the ground. Standard g = 9.80665 m/s² is a convention, not a measurement of local gravity.
07Common mistakes
Do not enter g as negative with this convention. Use the height mode only for a release from rest. A negative displacement in the time mode means the body is above its initial position.