Why does terminal velocity exist?
As speed increases, aerodynamic drag (∝ v²) increases until it equals gravitational weight. Net force = 0, so acceleration stops.
Terminal Velocity Calculator
v_t = √(2mg / ρC_D A)
Calculate terminal velocity from weight and drag. v_t = √(2mg/ρC_D A) — when drag equals gravity.
Calculate
Enter values above to calculate
How it calculates
1
g = 9.81 m/s² (gravitational acceleration)
2
v_t = √(2mg / (ρ × C_D × A))
3
Result in m/s
Formula
v_t = √(2mg / ρC_D A)
Variable Table
| Symbol | Quantity | SI Unit |
|---|---|---|
| v_t | Terminal velocity | m/s |
| m | Mass | kg |
| g | 9.81 | m/s² |
| ρ | Fluid density | kg/m³ |
| C_D | Drag coefficient | — |
| A | Cross-sectional area | m² |
How to Use This Calculator
This terminal velocity calculator is built for quick physics checks and worked-problem review. Enter values in the units shown beside each input, then compare the result with the formula and variable table before using it in a longer solution. The calculator does the arithmetic, but the physics still depends on choosing a model that matches the situation.
Start by identifying the system, the known quantities, and the quantity you want to find. If a value is given in a non-SI unit, convert it before substitution. A correct numerical answer with mixed units can still be physically wrong, especially when squared units, inverse seconds, charges, temperatures, or distances are involved.
Assumptions and Limits
The formula v_t = √(2mg / ρC_D A) is a model, not a universal description of every possible case. It assumes the quantities in the variable table are the relevant quantities for the problem and that hidden effects are either negligible or already included in the inputs. If friction, drag, relativistic speeds, changing fields, non-constant temperature, or geometry-specific effects matter, check whether a more complete model is needed.
Use the result as a magnitude and units check. Ask whether the answer has the right sign, whether it grows or shrinks when an input changes, and whether the limiting cases make sense. Setting an input to zero, doubling a quantity, or using a very large value is often enough to catch a formula choice or unit mistake before it reaches a final answer.
Worked Example
Skydiver: m=80 kg, ρ=1.225, C_D=1.0, A=0.5 m². Find terminal velocity.
Step 1: v_t = √(2×80×9.81 / (1.225×1.0×0.5))
Step 2: v_t = √(1569.6 / 0.6125)
Step 3: v_t = √2562
Answer: v_t ≈ 50.6 m/s ≈ 182 km/h
Common Mistakes
- At terminal velocity, net force = 0 (drag = weight)
- C_D for a skydiver spread-eagle ≈ 1.0; in dive position ≈ 0.7
- ρ_air at sea level ≈ 1.225 kg/m³
Related
Frequently Asked Questions
How do parachutes work?
Opening a parachute increases A dramatically, increasing drag and reducing terminal velocity from ~55 m/s to ~5–6 m/s for a safe landing.