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Physics

Terminal Velocity

v = √(2mg/ρACd). Free online Terminal Velocity. Calculate terminal velocity online — fast, accurate, mobile-friendly, no signup needed.

At terminal velocity, drag balances gravity.
v (m/s)
40.020403

Derivation

  1. ├── 01Givenm = 70, A = 0.7, Cd = 1, rho = 1.225
  2. ├── 02Formula√(2 × t × 9.81 / (r × a × n))
  3. └── 03Compute v (m/s)40.020403
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§01What is

Understanding the Terminal Velocity

The Terminal Velocity computes v (m/s) from 4 inputs: mass (kg), area (m²), drag coeff, density (kg/m³). v = √(2mg/ρACd).

Physics is the toolkit for turning a real-world observation into a prediction. Whether it’s a falling object, a moving car, or a stressed beam, the equations here are the same ones every engineer relies on. The Terminal Velocity sits in that toolkit — it v = √(2mg/ρACd). Enter your numbers above and the result updates instantly; every step of the math is shown in the Derivation panel so you can see exactly how the answer was reached.

§02The Formula

How it’s calculated

√(2 × t × 9.81 / (r × a × n))

Where

m
Mass (kg)
A
Area (m²)
Cd
Drag coeff
rho
Density (kg/m³)
§03Practical Example

Step-by-step walkthrough

Scenario

Apply the formula to a realistic set of inputs: Mass (kg) = 70, Area (m²) = 0.7, Drag coeff = 1, Density (kg/m³) = 1.225.

  1. 01Start by noting the input — Mass (kg): 70.
  2. 02Start by noting the input — Area (m²): 0.7.
  3. 03Start by noting the input — Drag coeff: 1.
  4. 04Start by noting the input — Density (kg/m³): 1.225.
  5. 05Substitute these values into the formula: √(2 × t × 9.81 / (r × a × n))
  6. 06Compute v (m/s): the calculator returns 40.0204.
  7. 07Cross-check the answer by opening the Derivation panel above — every line of math is shown so you can follow the computation end-to-end.
§04Variants

Common Terminal Velocity Problems

The formula gets rearranged depending on which variable you need. Here are the patterns you’ll run into in the real world — find the one that matches your problem and follow the worked steps.

01 · PATTERN

Mass (kg) halved

m = 35 (from 70)

Keep every other input at its default and halve the mass (kg). See how v (m/s) responds.

  1. 01New Mass (kg): 35
  2. 02Baseline v (m/s): 40.0204
  3. 03New v (m/s): 28.2987
  4. 04v (m/s) decreases by 29.3% → use this sensitivity to plan for real-world variation.
02 · PATTERN

Mass (kg) doubled

m = 140 (from 70)

Keep every other input at its default and double the mass (kg). See how v (m/s) responds.

  1. 01New Mass (kg): 140
  2. 02Baseline v (m/s): 40.0204
  3. 03New v (m/s): 56.5974
  4. 04v (m/s) increases by 41.4% → use this sensitivity to plan for real-world variation.
03 · PATTERN

Area (m²) halved

A = 0.35 (from 0.7)

Keep every other input at its default and halve the area (m²). See how v (m/s) responds.

  1. 01New Area (m²): 0.35
  2. 02Baseline v (m/s): 40.0204
  3. 03New v (m/s): 56.5974
  4. 04v (m/s) increases by 41.4% → use this sensitivity to plan for real-world variation.
04 · PATTERN

Area (m²) doubled

A = 1.4 (from 0.7)

Keep every other input at its default and double the area (m²). See how v (m/s) responds.

  1. 01New Area (m²): 1.4
  2. 02Baseline v (m/s): 40.0204
  3. 03New v (m/s): 28.2987
  4. 04v (m/s) decreases by 29.3% → use this sensitivity to plan for real-world variation.
§05FAQ

Frequently asked questions

Yes. The calculator implements the standard formula as documented and returns exact floating-point results. No approximations are used unless noted in the formula.
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