Quick answer
Terminal velocity is v_t = √(2mg ÷ (ρ A C_d)). An 80 kg skydiver with a frontal area of 0.7 m² and a drag coefficient of 1.0 in air of density 1.225 kg/m³ reaches 42.78 m/s, or 154 km/h.
Enter mass, frontal area, drag coefficient and fluid density. The calculator returns the terminal velocity in m/s and km/h.
Related tools: Acceleration Calculator: Average acceleration from change in velocity over time. SUVAT Calculator: Solve constant-acceleration motion for the missing quantities. Projectile Motion Calculator: Range, flight time and peak height of a projectile without air resistance.
How to use the Terminal Velocity Calculator
- Enter mass (kg) (above 0).
- Enter frontal area (m²) (above 0).
- Enter drag coefficient (above 0).
- Enter fluid density (kg/m³) (above 0). It starts at 1.225.
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Mass | A number, in kg | > 0 |
| Frontal area | A number, in m² | > 0 |
| Drag coefficient | A number | > 0 |
| Fluid density | A number, in kg/m³ | > 0, starts at 1.225 |
Formula and method
Formula
v_t = √(2mg ÷ (ρ A C_d))
IEEE-754 double precision; shown to the decimals indicated.
Default density is sea-level standard air (1.225 kg/m³, ISA).
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Mass = 80; Frontal area = 0.7; Drag coefficient = 1.0; Fluid density = 1.225.
| Result | Value |
|---|---|
| Terminal velocity | 42.7763 m/s |
| In km/h | 153.99 |
Example 2
Inputs: Mass = 0.145; Frontal area = 0.0043; Drag coefficient = 0.47; Fluid density = 1.225.
| Result | Value |
|---|---|
| Terminal velocity | 33.8929 m/s |
| In km/h | 122.01 |
Example 3
Inputs: Mass = 70; Frontal area = 0.2; Drag coefficient = 0.7; Fluid density = 1.0.
| Result | Value |
|---|---|
| Terminal velocity | 99.0285 m/s |
| In km/h | 356.5 |
The first line is the headline result (terminal velocity). Below it the terminal Velocity Calculator lists in km/h, which describe the same case from other angles. IEEE-754 double precision; shown to the decimals indicated.
Where it comes from
At terminal velocity, drag ½ρv²AC_d equals weight mg, so the acceleration is zero. A belly-down skydiver has a larger area (about 0.7 m²) than a head-down one (0.2 m²), which falls at roughly 70 to 85 m/s.
Where this estimate stops applying
The drag coefficient depends on shape and speed, so the result is an estimate. Density falls with altitude, raising terminal velocity. A parachute with a large area reduces it to about 5 m/s.
How the result changes with mass
Holding every other input at the first worked example, this table changes only mass. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Mass | Terminal velocity | In km/h |
|---|---|---|
| 40 | 30.2474 m/s | 108.89 |
| 80 | 42.7763 m/s | 153.99 |
| 160 | 60.4948 m/s | 217.78 |
| 320 | 85.5526 m/s | 307.99 |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Mass: entering "0" shows "Mass must be greater than 0." beside that field and no result.
- Drag coefficient: entering "0" shows "Drag coefficient must be greater than 0." beside that field and no result.
Choosing between the Terminal Velocity Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Acceleration Calculator](/science/acceleration-calculator/) | initial velocity, final velocity and time | Acceleration |
| [SUVAT Calculator](/science/suvat/) | you know and initial velocity u | Final velocity v |
| [Projectile Motion Calculator](/science/projectile-motion-calculator/) | launch speed and launch angle | Range |
| [Free Fall Calculator](/science/free-fall-calculator/) | i know the and height or time | Fall time |
| [Magnitude of Acceleration Calculator](/science/magnitude-of-acceleration-calculator/) | x component and y component | Magnitude |
Background: motion and mechanics
For constant acceleration the standard relations are v = u + at, s = ut + ½at², v² = u² + 2as and s = ½(u + v)t. Pick the equation that contains your three known quantities and the one you want. Use SI units (metres, seconds, kilograms, newtons, joules) throughout or the answer will be off by a factor.
These equations stop applying when acceleration changes during the motion, as with a rocket burning fuel; that needs calculus or numerical methods.
Assumptions and limitations
- Drag coefficient depends on shape and speed
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for mass and drag coefficient to confirm this.
Frequently asked questions
What is the terminal velocity of a raindrop?
About 9 m/s for large drops.
Does mass change it?
Yes, heavier objects fall faster.
What is C_d?
A shape-dependent drag factor.
What does the Terminal Velocity Calculator calculate?
Terminal speed of a falling object from mass, area and drag coefficient. It returns Terminal velocity and In km/h.
What formula does the Terminal Velocity Calculator use?
v_t = √(2mg ÷ (ρ A C_d)). Default density is sea-level standard air (1.225 kg/m³, ISA).
What do I need to enter in the terminal Velocity Calculator?
You enter Mass (kg), Frontal area (m²), Drag coefficient and Fluid density (kg/m³).
How is the result rounded or limited?
IEEE-754 double precision; shown to the decimals indicated. Drag coefficient depends on shape and speed.
What is an example of a terminal Velocity result?
With mass 80, frontal area 0.7, drag coefficient 1.0 and fluid density 1.225, the terminal velocity is 42.7763 m/s.
Where does the method come from?
The method follows: ICAO International Standard Atmosphere (sea-level density 1.225 kg/m³); CODATA 2018 / SI exact constants: g₀ = 9.80665 m/s², c = 299,792,458 m/s, h = 6.62607015×10⁻³⁴ J·s, e = 1.602176634×10⁻¹⁹ C, G = 6.67430×10⁻¹¹ m³/(kg·s²).
Related calculators
- Acceleration Calculator — Average acceleration from change in velocity over time.
- SUVAT Calculator — Solve constant-acceleration motion for the missing quantities.
- Projectile Motion Calculator — Range, flight time and peak height of a projectile without air resistance.
- Free Fall Calculator — Fall time, height and impact speed in free fall from rest.
- Magnitude of Acceleration Calculator — Magnitude of an acceleration vector from its components.
- Angular Velocity Calculator — Angular velocity from rpm, frequency, or an angle and time.
- Escape Velocity Calculator — Speed needed to escape a body's gravity from its surface.
Sources
- ICAO International Standard Atmosphere (sea-level density 1.225 kg/m³); CODATA 2018 / SI exact constants: g₀ = 9.80665 m/s², c = 299,792,458 m/s, h = 6.62607015×10⁻³⁴ J·s, e = 1.602176634×10⁻¹⁹ C, G = 6.67430×10⁻¹¹ m³/(kg·s²)
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.