What equation does this calculator solve?

It uses y(t) = h + v0t - 1/2 gt² for 1D vertical motion and picks the physically meaningful non-negative root when the object reaches the ground again.

How is this different from the projectile motion calculator?

This page is only for vertical motion. There is no launch angle, no horizontal range, and no flat-ground 2D arc. Use Projectile Motion when you need both horizontal and vertical components.

What sign convention does it use?

Upward is positive and downward is negative. If you do not want to think in signs, switch to the direction + magnitude input mode and let the calculator build the signed velocity for you.

Why do peak height and time to peak disappear sometimes?

Those outputs only apply when the initial vertical velocity is upward. For a drop from rest or a downward throw, the object starts at its highest point, so there is no upward phase to report.

Are these results realistic for safety or testing?

No. This is an idealized no-drag model for homework, lab intuition, and rough checks. It does not include air resistance, terminal velocity, terrain, or material safety limits.

Free Fall Calculator

Calculate time to impact, impact speed, peak height, and time to peak for a vertical drop or throw. Built for homework, lab intuition, and rough no-drag checks.

How It Works

Formula

y(t) = h + v_0 t - \frac{1}{2} g t^2

t_{impact} = \frac{v_0 + \sqrt{v_0^2 + 2gh}}{g}

v_{impact} = v_0 - g t_{impact}

t_{peak} = \frac{v_0}{g}

h_{peak} = h + \frac{v_0^2}{2g}

Enter a starting height, an initial vertical velocity, and gravity. The calculator models only vertical motion above a flat ground reference. Time to impact comes from the positive ground-contact root, while impact speed comes from the downward velocity magnitude at that time.

The calculator treats upward as positive and gravity as a constant downward acceleration. It solves the quadratic 0 = h + v_0 t - 1/2 gt^2 by taking the non-negative root t = (v_0 + sqrt(v_0^2 + 2gh)) / g. Impact velocity then follows from v = v_0 - gt, and the page reports its magnitude as impact speed. When v_0 > 0, the object first rises to a peak at t_peak = v_0 / g and h_peak = h + v_0^2 / (2g). No air resistance or horizontal motion is included.

Frequently Asked Questions

Related Calculators

Projectile Motion Calculator

Compute range, max height, and flight time for projectiles

Kinetic Energy Calculator

Compute KE = 1/2 mv² from mass and velocity

Potential Energy Calculator

Compute PE = mgh from mass, gravity, and height

Speed, Distance & Time Calculator

Compute speed, distance, or time from two known values

Free Fall Calculator

How It Works

Frequently Asked Questions

Related Calculators

All calculators

Ready to Calculate?