Physics · 5 min read
How Free Fall Distance Grows with Time
s = ½ g t² from rest — distance grows with time squared
In free fall from rest, ignoring air resistance, the distance fallen is half g times time squared. This tutorial walks through s = ½ g t² and v = g t, a 2 s / 9.80665 m/s² worked example matching the Free Fall Calculator, and a height-versus-time sketch that substitutes your t.
Written by the My Calculator Stack editorial team. About our methods
This model starts from rest and ignores air resistance. Real drops reach a terminal speed; treat the numbers as an ideal kinematics sketch, not a field measurement.
1.What free fall from rest is
Free fall here means motion under gravity alone, starting from rest. The only acceleration is g, taken as constant near Earth’s surface. Distance fallen grows faster than linearly: twice the time means four times the drop. Impact speed grows linearly: twice the time means twice the speed. Air drag, buoyancy, and a nonzero launch speed are outside this identity.
2.The formula
From rest, distance is s = ½ g t² and impact speed is v = g t. Time t is in seconds; g is in m/s² (Earth default 9.80665). Both s and v are zero at t = 0. The same pair powers the Free Fall Calculator on this site. If you already know s, you can rearrange: t = √(2s/g).
\[ s=\tfrac12 gt^{2},\quad v=gt \]
3.Worked example
Take t = 2 s and g = 9.80665 m/s² — the same defaults as the Free Fall Calculator. Then s = ½ × 9.80665 × 2² = ½ × 9.80665 × 4 ≈ 19.61 m, and v = 9.80665 × 2 ≈ 19.61 m/s. At 1 s the drop is only about 4.90 m; at 4 s it is about 78.45 m, four times the 2 s distance because time squared.
\[ s=\tfrac12(9.80665)(2)^{2}\approx 19.61 \]
4.Height-versus-time playground
Move fall time (and g if you want) to substitute t into s = ½ g t². The sketch plots distance fallen against time — a parabola — with a marker at your current t. This is a teaching widget — no favorites, no full calculator chrome. Open the Free Fall Calculator when you want the standalone tool.
Inline playground
Distance fallen s
19.61 m
Impact speed v
19.61 m/s
s = ½×9.80665×2² ≈ 19.61
Teaching sketch only — from rest, constant g, no air resistance.
Open the full Free Fall calculator →5.Open the full calculator
The Free Fall Calculator uses the same s = ½ g t² and v = g t pair, the same 2 s / 9.80665 m/s² example, and How it works plus FAQ on one page. Browse other physics calculators if you need displacement, drag, or impact-style checks next.
Try it yourself
Open the related calculator and put these formulas to work.