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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.

Units
cm
m/s
m/s²
Examples

Drop from 36 m with zero initial vertical velocity to get the impact time and speed immediately.

Time to impact
2.7091 s
Impact speed
26.5767 m/s

Dropped from rest — impact speed comes entirely from gravity acting over the starting height.

Idealized no-drag physics result for homework, lab intuition, and rough checks. Not a safety guarantee or drop-test recommendation.

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Examples

How It Works

Formula

y(t)=h+v0t−12gt2y(t) = h + v_0 t - \frac{1}{2} g t^2

timpact=v0+v02+2ghgt_{impact} = \frac{v_0 + \sqrt{v_0^2 + 2gh}}{g}

vimpact=v0−gtimpactv_{impact} = v_0 - g t_{impact}

tpeak=v0gt_{peak} = \frac{v_0}{g}

hpeak=h+v022gh_{peak} = h + \frac{v_0^2}{2g}

Variables

y(t)y(t)

Height above the ground at time t

hh

Starting height above ground(m or ft)

v0v_0

Initial vertical velocity (upward positive)(m/s or ft/s)

gg

Gravity magnitude(m/s² or ft/s²)

timpactt_{impact}

Time when the object reaches the ground again(s)

hpeakh_{peak}

Highest point above ground, if there is an upward phase(m or ft)

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

01What 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.
02How 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.
03What 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.
04Why 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.
05Are 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.

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