Terminal Velocity Calculator
Terminal fall speed from mass, area, and shape.
What it does
Falling objects stop accelerating when drag meets weight. An 80 kg spread-eagle skydiver settles at 42.78 m/s (95.7 mph) while the same body head-first at smaller area nears 98 m/s. Mass, area, and shape set the ceiling together.
The tool above runs the NASA drag balance. Enter mass, frontal area, and shape, and it prints terminal speed in m/s, mph, and km/h. Defaults show the spread skydiver; 60 kg matches 37.05 m/s while head-first runs far faster.
Flight research centers agree. NASA Glenn derives Vt from weight-equals-drag with g at 9.8, Georgia Tech prints the identical root with 1.225 air density and worked spheres, and UCF checks head-first at 98 m/s with spread-eagle at 44. Sea-level air anchors all three.
Posture is the biggest lever a skydiver owns. Tucking from spread to head-first quarters the area-drag product and more than doubles speed, which is why tracking suits exist. Altitude thins air further; sea-level numbers understate high jumps.
How to use
- Enter the mass in kg.
- Enter the frontal area in m2.
- Pick the drag shape.
- Read m/s first, then mph.
- Read km/h beside it.
- Adjust area for posture.
Formula
- m
- Falling mass in kg.
- A
- Frontal area in m2.
- Cd
- Shape drag number, 0.47 to 1.0 here.
NASA Glenn sets W=D with Vt from the drag equation; Georgia Tech and UCF print identical forms with worked skydiver checks.
Worked example
Example: 80 kg skydiver
Defaults: 80 kg spread-eagle skydiver.
- Inputs: 80 kg skydiver, 0.7 m2, Cd 1.0.
- Numerator: 2 x 80 x 9.81 = 1569.6.
- Denominator: 1.225 x 0.7 x 1.0 = 0.8575.
- Speed: sqrt(1569.6 / 0.8575) = 42.78 m/s.
- MPH 95.7, km/h 154. Tool shows 42.78 m/s.
Reference table
| Case | m/s | mph |
|---|---|---|
| 80 kg spread | 42.78 | 95.7 |
| 60 kg spread | 37.05 | 82.9 |
| 75 kg head-first | 97.64 | 218.4 |
Limits
- Steady fall only. Acceleration phase excluded.
- Sea-level air; altitude differs.
- Fixed shape assumed; tumbling varies.
- No wind or updraft effects.
Common mistakes
- Forgetting area units in m2.
- Using diameter instead of area.
- Mixing mph with m/s mid-chain.
- Ignoring posture changes everything.
- Applying sea-level air at altitude.
Try it yourself
Quick checks. Answers sit tucked under each question.
60 kg skydiver, same shape?
Numerator 2 x 60 x 9.81 = 1177.2. Denominator 0.8575. v = sqrt(1372.83) = 37.05 m/s. MPH 82.9.
75 kg head-first (0.18 m2, Cd 0.7)?
Numerator 2 x 75 x 9.81 = 1471.5. Denominator 1.225 x 0.18 x 0.7 = 0.15435. v = sqrt(9533.06) = 97.64 m/s, 218.4 mph.
Questions
How is terminal velocity figured?
Root of 2mg over (rho x A x Cd). Here sqrt(1569.6/0.8575) = 42.78 m/s.
How do m/s convert?
Times 2.23694: 42.78 m/s is 95.7 mph. Times 3.6 for km/h: 154.
What air density?
Sea-level 1.225 kg/m3 here. Altitude thins air and raises speed.
What drag coefficients?
Flat plate 1.12, spread human 1.0, head-first 0.7, sphere 0.47, airfoil 0.05.
Does weight matter?
Yes. Heavier falls faster at equal shape: 60 kg matches 37.05 m/s here.
What about the speeding-up phase?
Yes. This page models steady fall only, not the acceleration seconds before.
Sources
- NASA Glenn: Flight Equations with Drag (Vt form)
- Georgia Tech: Terminal Speed (1.225 density)
- UCF Physics 6.4: Drag and Terminal Speed