# Free Fall with Air Resistance Calculator

URL: https://speedycalculator.com/calculators/physics/free-fall-air-resistance/
Last updated: 2026-10-30

> The free fall with air resistance calculator finds the fall time, the speed when hitting the ground and the terminal velocity of a falling object with quadratic drag – from a drag constant or from the cross-section, drag coefficient and air density.

## Inputs

- Mass (kg, g, mg, t, lb, oz)
- Altitude (fall height) (m, cm, mm, km, in, ft, yd, mi)
- Gravitational acceleration g (m/s², ft/s², g, cm/s²)
- Air resistance from…
- Air resistance coefficient k (kg/m)
- Cross-section area (m², cm², mm², km², in², ft²)
- Drag coefficient C_d
- Medium density ρ (kg/m³, g/cm³, g/mL, lb/ft³, lb/in³)
- Speed for drag force (m/s, km/h, mph, ft/s, knots, km/s)

## Results

- Terminal velocity
- Time of fall
- Speed at the ground
- Drag force at the chosen speed
- Air resistance coefficient k (kg/m)

## Formula

```
k = ½ρC_dA,  v_t = √(mg/k)
t = (v_t/g)·arcosh(e^{hk/m}),  v = v_t·tanh(g t / v_t)
```

## Explanation

Real falling objects reach a terminal velocity where drag balances weight: about 55 m/s (200 km/h) for a skydiver belly-down, but only a few m/s for a raindrop. This calculator solves the exact equations of motion for drag proportional to speed squared.

### How to use the Free Fall with Air Resistance Calculator

- **Mass**
- **Altitude (fall height)**
- **Gravitational acceleration g**
- **Air resistance from…**
- **Air resistance coefficient k (kg/m)**
- **Cross-section area**
- **Drag coefficient C_d**
- **Medium density ρ**
- **Speed for drag force**

Results update as you type, every field has its own unit menu, and everything is calculated in your browser.

### How it works

Choose whether to enter the air resistance coefficient k directly or to build it from area, drag coefficient and air density. The calculator also gives the drag force at any speed you choose.

### Inputs explained

FieldWhat to enterMassUnits: kg, g, mg, t, lb, ozAltitude (fall height)Units: m, cm, mm, km, in, ft …Gravitational acceleration gUnits: m/s², ft/s², g, cm/s²Air resistance from…Choose one: Coefficient k, Area, drag coefficient and densityAir resistance coefficient k (kg/m)A numberCross-section areaUnits: m², cm², mm², km², in², ft²Drag coefficient C_dA numberMedium density ρUnits: kg/m³, g/cm³, g/mL, lb/ft³, lb/in³Speed for drag forceUnits: m/s, km/h, mph, ft/s, knots, km/s

### What each result means

- **Terminal velocity** = sqrt([Mass]×[Gravitational acceleration g]÷[k])
- **Time of fall** = [Terminal velocity]÷[Gravitational acceleration g]×ln(exp([Altitude (fall height)]×[k]÷[Mass]) + sqrt(exp(2×[Altitude (fall height)]×[k]÷[Mass]) - 1))
- **Speed at the ground** = [Terminal velocity]×(exp(2×[Gravitational acceleration g]×[Time of fall]÷[Terminal velocity]) - 1)÷(exp(2×[Gravitational acceleration g]×[Time of fall]÷[Terminal velocity]) + 1)
- **Drag force at the chosen speed** = [k]×[Speed for drag force]^2
- **Air resistance coefficient k (kg/m)** = [k]

### Example values

How the main result changes when **Mass** changes and everything else stays at the example values above:

Mass (kg)Time of fall (s)37.531.04256.2526.3567523.69993.7521.977112.520.77115019.199

## Worked example

Inputs — Mass: 75 kg; Altitude (fall height): 1,000 m; Gravitational acceleration g: 9.80665 m/s²; Air resistance from…: Area, drag coefficient and density; Cross-section area: 0.7 m²; Drag coefficient C_d: 0.7; Medium density ρ: 1.225 kg/m³; Speed for drag force: 30 m/s.

Results — Terminal velocity = 178.214 km/h; **Time of fall = 23.699 s**; Speed at the ground = 178.184 km/h; Drag force at the chosen speed = 270.112 N; Air resistance coefficient k (kg/m) = 0.30013.

## Key terms

- **Drag coefficient**: A shape factor for air resistance.

## FAQ

**What is terminal velocity?**
The speed at which drag equals weight, so the object stops accelerating.

**How fast does a skydiver fall?**
About 200 km/h belly-down, faster head-down.

**Why use the speed squared?**
At everyday speeds and sizes, air drag grows roughly with the square of speed.

**Does a heavier object fall faster with air resistance?**
Yes, for the same shape – it needs more drag to balance its weight.


## Sources

- [OpenStax – University Physics Volume 1](https://openstax.org/details/books/university-physics-volume-1)
- [NASA Glenn – Terminal velocity](https://www.grc.nasa.gov/www/k-12/airplane/termv.html)