Aerodynamic Drag Force & Free-Fall Terminal Velocity Calculator

Compute terminal velocity v_t = √(2mg / ρCdA) and dynamic drag force.

Terminal Free-Fall Velocity
57.68 m/s
Terminal Speed in km/h 207.65 km/h
Terminal Speed in mph 129.03 mph
Equilibrium Drag Force (Weight) 784.53 N
Inputs
kg
Falling or moving body mass in kilograms.
C_d
Dimensionless drag coefficient (C_d).
m²
Frontal projected cross-sectional area in square meters.
kg/m³
Air or fluid density in kg/m³ (1.225 sea-level air).
Results & Graph
Terminal Free-Fall Velocity
57.68 m/s
Terminal Speed in km/h
207.65 km/h
Terminal Speed in mph
129.03 mph
Equilibrium Drag Force (Weight)
784.53 N

Terminal Free-Fall Velocity

Graph 1 • Mass Kg Sensitivity Recalculates the domain equation across 50% to 150% of the primary input while holding other parameters constant.
0 m/s 38.1 m/s 76.3 m/s 50%: 40.79 m/s 40.8 50% 75%: 49.95 m/s 50.0 75% 100%: 57.68 m/s 57.7 100% 125%: 64.49 m/s 64.5 125% 150%: 70.64 m/s 70.6 150%
Graph 2 • Primary & Supporting Metric Comparison Compares the primary output alongside supporting domain benchmarks.
Terminal Free-Fall Velocity 57.68 m/s Terminal Speed in km/h 207.65 km/h Terminal Speed in mph 129.03 mph Equilibrium Drag Force (Weight) 784.53 N
Graph 3 • Exact Output Table & Units Displays each calculated output in its exact domain unit.
Terminal Free-Fall Velocity57.68 m/sTerminal Speed in km/h207.65 km/hTerminal Speed in mph129.03 mphEquilibrium Drag Force (Weight)784.53 N
Summary: An 80 kg body (Cd=0.7, A=0.55 m²) reaches terminal equilibrium at 57.68 m/s (207.6 km/h or 129 mph).
Summary: An 80 kg body (Cd=0.7, A=0.55 m²) reaches terminal equilibrium at 57.68 m/s (207.6 km/h or 129 mph).
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Formula & Mathematical Methodology: Terminal Velocity & Drag Physics & Engineering Equation

vterminal = 2 × m × gρ × Cd × A
Fdrag = 0.5 × ρ × v² × Cd × A
v_terminal = √[ (2 × m × g) / (ρ × C_d × A) ]; F_drag = 0.5 × ρ × v² × C_d × A
  • massKg: Mass Kg (kg)
  • dragCoefficientCd: Drag Coefficient Cd (C_d)
  • crossSectionalAreaM2: Cross Sectional Area M2 (m²)
  • fluidDensityKgM3: Fluid Density Kg M3 (kg/m³)

Rounding: Physical constants follow CODATA/NIST values; output quantities display to 2 decimal places.

Worked Example: Physics & Engineering Benchmark: Terminal Velocity & Drag

Compute terminal velocity v_t = √(2mg / ρCdA) and dynamic drag force.

  1. Enter the physical dimensions, electrical parameters, or thermodynamic state variables.
  2. Apply the governing equation: v_terminal = √[ (2 × m × g) / (ρ × C_d × A) ]; F_drag = 0.5 × ρ × v² × C_d × A.
  3. Inspect the primary SI output, derived quantities, and 3 visual SVG graphs.
Result: Computes Terminal Velocity & Drag via v_terminal = √[ (2 × m × g) / (ρ × C_d × A) ]; F_drag = 0.5 × ρ × v² × C_d × A.

Frequently Asked Questions

What equation powers the Aerodynamic Drag Force & Free-Fall Terminal Velocity Calculator?

It evaluates v_terminal = √[ (2 × m × g) / (ρ × C_d × A) ]; F_drag = 0.5 × ρ × v² × C_d × A using IEEE-754 double precision and renders three synchronized SVG plots.

Can I test parameter sensitivity across multiple values?

Yes. Graph 1 automatically plots a 50%–150% parameter response curve, and you can pin up to 3 custom scenarios.

Are all units consistent with SI standards?

Yes. Each input field specifies its exact SI or engineering unit and converts internally where needed.

Science & Engineering · Fluid Mechanics & Hydraulics

Aerodynamic Drag Force & Free-Fall Terminal Velocity Calculator: inputs, method, and how to read the result

Compute terminal velocity v_t = √(2mg / ρCdA) and dynamic drag force.

Choose inputs for the case you are checking

The defaults are illustrative. Replace them with values for your case and keep the units shown beside each field.

  • Mass Kg: Falling or moving body mass in kilograms.
  • Drag Coefficient Cd: Dimensionless drag coefficient (C_d).
  • Cross Sectional Area M2: Frontal projected cross-sectional area in square meters.
  • Fluid Density Kg M3: Air or fluid density in kg/m³ (1.225 sea-level air).

What the calculation includes

With the default values shown, Terminal Free-Fall Velocity is 57.68 m/s. The calculation follows Terminal Velocity & Drag Physics & Engineering Equation; the formula and variable definitions above show how the inputs combine.

One-input check: With the other defaults held constant, changing Mass Kg from 80 kg to 88 kg changes Terminal Free-Fall Velocity from 57.68 m/s to 60.49 m/s. This is a comparison inside the calculator's stated model, not a prediction.

Where to use caution

  • Uses standard SI physical constants (g = 9.80665 m/s², c = 299,792,458 m/s, σ = 5.670374×10⁻⁸ W·m⁻²·K⁻⁴).
  • Engineering reference model; apply appropriate safety factors and empirical calibration for critical hardware designs.

Scope: SI / NIST Physics & Engineering Standard Check the assumptions and limitations against your situation before relying on the estimate.

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