Vertical Motion Calculator

How it works

1. 1Enter the initial upward velocity v₀ and the elapsed time t.
2. 2The calculator applies v = v₀ − gt and y = v₀t − ½gt² using standard gravity (9.81 m/s²).
3. 3Results show the height above the launch point, current velocity (negative when falling), maximum height, and time to reach the apex.

Use cases

• Physics students verifying hand-worked kinematics problems on vertical throws.
• Sports scientists estimating ball height and hang time from a measured launch speed.
• Engineers checking safety clearances for vertically launched payloads or test articles.

Frequently asked questions

What formulas does this calculator use?

Two kinematics equations under constant gravitational acceleration g = 9.81 m/s²: velocity v = v₀ − gt, and height y = v₀t − ½gt². The maximum height follows from setting v = 0: y_max = v₀² ÷ (2g). Time to apex is t_apex = v₀ ÷ g.

How do I read a negative velocity result?

Velocity is positive while the object rises and negative once it passes the apex and falls back down. For example, thrown up at 20 m/s it reaches the apex after ≈ 2.04 s at ≈ 20.4 m; at t = 3 s the velocity is 20 − 9.81 × 3 ≈ −9.4 m/s (descending).

Does the calculator account for air resistance?

No. The model assumes a vacuum (no drag), a good approximation for dense, slow-moving objects over short distances. For light or fast objects, real heights and velocities are noticeably lower.