🪂 Terminal Velocity Calculator
Calculate terminal speed
How to Use This Calculator
Enter Mass
Input the mass of the falling object, measured in kilograms (kg). Heavier objects have higher terminal velocities because they experience more gravitational force relative to air resistance.
Enter Cross-Sectional Area
Input the cross-sectional area perpendicular to the direction of fall, measured in square meters (m²). Larger area means more air resistance and lower terminal velocity. For a person in freefall, typical area is 0.7 m².
Enter Drag Coefficient
Input the drag coefficient (C_d), a dimensionless value that depends on the object's shape. Typical values: 0.47 for a sphere, 0.5-1.2 for irregular objects, 1.0-1.3 for a person. Lower values mean less drag.
Enter Air Density
Input the air density, measured in kg/m³. Default is 1.225 kg/m³ (sea level at 15°C). Higher altitude = lower density = higher terminal velocity. At 10,000 m altitude, density ≈ 0.4 kg/m³.
Set Gravity (Optional)
Default gravity is 9.81 m/s² (Earth). You can change this for calculations on other planets. Lower gravity means lower terminal velocity.
Click Calculate
Press the "Calculate Terminal Velocity" button to compute the terminal velocity, which is the maximum constant speed the object reaches when air resistance balances gravity.
Formula
v_terminal = √(2mg / (C_d × ρ × A))
Where:
v_terminal = Terminal velocity (m/s)
m = Mass (kg)
g = Gravitational acceleration (9.81 m/s²)
C_d = Drag coefficient (dimensionless)
ρ = Air density (kg/m³)
A = Cross-sectional area (m²)
This formula assumes the drag force F_drag = ½ρC_dAv² balances weight mg.
Example 1: Skydiver in freefall
Given: m = 70 kg, A = 0.7 m², C_d = 1.0, ρ = 1.225 kg/m³, g = 9.81 m/s²
v_terminal = √(2 × 70 × 9.81 / (1.0 × 1.225 × 0.7))
v_terminal = √(1373.4 / 0.8575)
v_terminal = √1602.3
v_terminal = 40.03 m/s ≈ 144 km/h
A typical skydiver reaches terminal velocity around 200 km/h (55 m/s), but this is for a spread-eagle position with more drag.
Example 2: Raindrop falling
Given: m = 0.00001 kg (0.01 g), A = π(0.001)² = 3.14×10⁻⁶ m², C_d = 0.47 (sphere), ρ = 1.225 kg/m³
v_terminal = √(2 × 0.00001 × 9.81 / (0.47 × 1.225 × 3.14×10⁻⁶))
v_terminal = √(0.0001962 / 1.81×10⁻⁶)
v_terminal = √108.4
v_terminal = 10.41 m/s ≈ 37 km/h
Small raindrops fall at about 9-10 m/s, while large raindrops can reach 20 m/s.
Understanding Terminal Velocity
• Terminal velocity occurs when drag force equals weight: mg = ½ρC_dAv²
• Heavier objects (larger m) have higher terminal velocity
• Larger cross-sectional area (A) decreases terminal velocity
• Higher air density (ρ) decreases terminal velocity
• Lower drag coefficient (C_d) increases terminal velocity
• At terminal velocity, acceleration is zero (constant speed)
About Terminal Velocity Calculator
The Terminal Velocity Calculator is a physics tool for calculating the maximum constant speed reached by a falling object when air resistance balances gravitational force. Terminal velocity occurs when the upward drag force equals the downward gravitational force, resulting in zero net force and constant velocity. This calculator uses the formula v_terminal = √(2mg / (C_d × ρ × A)), which accounts for the object's mass, gravitational acceleration, drag coefficient, air density, and cross-sectional area. Understanding terminal velocity is crucial for analyzing freefall, skydiving, parachuting, and any scenario involving falling objects with air resistance.
When to Use This Calculator
- Physics Problems: Solve problems involving falling objects with air resistance
- Skydiving Analysis: Calculate terminal velocities for skydivers in different body positions
- Safety Planning: Determine maximum speeds for falling objects in safety assessments
- Engineering Design: Analyze terminal velocities for parachutes, objects dropped from aircraft, or falling mechanisms
- Educational Purposes: Understand how air resistance affects falling objects and learn about terminal velocity
- Meteorology: Calculate terminal velocities for raindrops, hailstones, or other falling particles
Why Use Our Calculator?
- ✅ Comprehensive Formula: Uses the complete terminal velocity equation accounting for all factors
- ✅ Real-World Values: Includes default values for common scenarios (air density, drag coefficients)
- ✅ Multiple Parameters: Accounts for mass, area, drag coefficient, air density, and gravity
- ✅ Educational Value: Shows the formula and step-by-step calculations for learning
- ✅ Flexible Input: Adjust all parameters for different scenarios and conditions
- ✅ Dual Units: Displays results in both m/s and km/h for convenience
Common Applications
Skydiving and Parachuting: Calculate terminal velocities for skydivers in different body positions. Spread-eagle position has higher drag and lower terminal velocity (~200 km/h) than head-down position (~300 km/h).
Physics Education: Help students understand how air resistance affects falling objects and how terminal velocity is reached when forces balance. Demonstrates the relationship between object properties and terminal velocity.
Meteorology: Calculate terminal velocities for precipitation particles. Raindrops typically fall at 9-20 m/s depending on size, while hailstones can reach much higher velocities.
Safety Engineering: Determine maximum speeds for objects dropped from heights, helping design safety systems and assess impact forces.
Tips for Best Results
- Drag Coefficients: Use C_d = 0.47 for spheres, 0.5-1.2 for irregular objects, 1.0-1.3 for humans
- Air Density: Standard sea level is 1.225 kg/m³; decreases with altitude (0.4 kg/m³ at 10,000 m)
- Cross-Sectional Area: Use the area perpendicular to fall direction; for humans, ~0.7 m² spread-eagle, ~0.18 m² head-down
- Reynolds Number: This formula assumes turbulent flow; for very small objects, Stokes' law may be more appropriate
- Real-World Variation: Actual terminal velocities vary due to body position changes, air currents, and other factors
Frequently Asked Questions
What is terminal velocity?
Terminal velocity is the maximum constant speed reached by a falling object when air resistance (drag) equals gravitational force. At this point, net force is zero, so acceleration is zero and velocity is constant. The object continues falling at this speed until it hits the ground.
Why do heavier objects have higher terminal velocity?
Heavier objects experience more gravitational force (weight = mg). To balance this larger force, they need more air resistance, which requires higher speed. Since drag force increases with velocity squared, heavier objects reach higher terminal velocities to generate enough drag to balance their greater weight.
How does body position affect terminal velocity for skydivers?
Body position changes cross-sectional area and drag coefficient. Spread-eagle position: A ≈ 0.7 m², C_d ≈ 1.0, v_terminal ≈ 55 m/s (200 km/h). Head-down position: A ≈ 0.18 m², C_d ≈ 0.7, v_terminal ≈ 88 m/s (320 km/h). Smaller area and lower drag = higher terminal velocity.
Does air density affect terminal velocity?
Yes! Higher air density increases drag force, so terminal velocity is lower. At sea level (ρ = 1.225 kg/m³), terminal velocity is lower than at high altitude (ρ ≈ 0.4 kg/m³ at 10,000 m). This is why skydivers fall faster at higher altitudes before reaching denser air.
What's the terminal velocity of a human?
For a typical person (70 kg) in spread-eagle position: ~55 m/s (200 km/h). In head-down position: ~88 m/s (320 km/h). With a parachute open: ~5-7 m/s (18-25 km/h). Actual values vary with body size, position, and equipment.
Can terminal velocity be reached in a vacuum?
No. Terminal velocity requires air resistance. In a vacuum (no air), there's no drag force, so objects continue accelerating due to gravity until they hit the ground. Terminal velocity only exists when air resistance is present.