Free Fall Calculator
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Ignoring air resistance, a dropped object falls \(d = \tfrac{1}{2}gt^{2}\) and reaches speed \(v = gt\). From 20 m it lands after \(t = \sqrt{2h/g} \approx 2.02\) s at about 19.8 m/s (71 km/h).
Height above the ground during the fall.
| Fall time | 2.01962 s |
| Distance | 20 m = 65.6168 ft |
| Final speed | 19.8057 m/s = 71.3005 km/h = 44.3041 mph |
| Average speed | 9.90285 m/s |
Show steps
- Height h = 20 m, initial downward speed v₀ = 0 m/s, g = 9.80665 m/s².
- Solve \(h = v_{0}t + \tfrac{1}{2}gt^{2}\) for t: \(t = \frac{-v_{0} + \sqrt{v_{0}^{2} + 2gh}}{g} = 2.01962\ \text{s}\)
- Impact speed: \(v = v_{0} + gt = 19.8057\ \text{m/s}\)
How to use the free fall calculator
- Choose whether you know the height or the time.
- Enter it with units, an initial downward speed if the object is thrown down, and the gravity.
- Press Calculate to get the time, distance, impact speed and a height–time graph.
Free fall equations
- \(d = v_{0}t + \tfrac{1}{2}gt^{2}\)
- \(v = v_{0} + gt\)
- \(v^{2} = v_{0}^{2} + 2gd\)
- Dropped from rest: \(t = \sqrt{\frac{2h}{g}}\) and \(v = \sqrt{2gh}\)
Worked example
A stone dropped from 45 m: \(t = \sqrt{\frac{2 \times 45}{9.80665}} \approx 3.03\) s, \(v = 9.80665 \times 3.03 \approx 29.7\) m/s. Each second it falls farther than the second before: about 4.9 m, then 14.7 m, then 24.5 m.
Air resistance
These formulas assume no air resistance. Real objects reach a terminal velocity when drag balances weight: about 55 m/s for a skydiver lying flat, and only a few meters per second for a feather or leaf.
Free fall practice quiz: 10 questions
Test yourself with 10 multiple-choice questions. Choose an answer and press Submit to see if you are right and why. Your score appears at the end.
Quiz complete
Frequently asked questions
How long does it take to fall from a height?
From rest and without air resistance, t = √(2h/g). From 20 m on Earth that is about 2.02 s.
How fast does an object hit the ground?
v = √(2gh) when dropped from rest. From 20 m it is about 19.8 m/s.
Does mass affect the fall time?
Not without air resistance: all objects accelerate at g. With air, light and broad objects fall more slowly.
What value of g should I use?
Standard gravity is 9.80665 m/s²; many textbooks round to 9.8 or 9.81. The calculator also has the Moon, Mars and Jupiter.
Does this include air resistance?
No. It gives the ideal (vacuum) result, which is accurate for dense objects over short falls.
Sources
- OpenStax University Physics Volume 1
- OpenStax College Physics 2e
- NIST Special Publication 811: Guide for the Use of the SI
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