Free Fall Height Calculator
Calculate the maximum height reached during free fall motion using time, velocity, or initial conditions
Calculate Free Fall Height
Duration of the free fall motion
Starting velocity (0 for objects dropped from rest)
Gravitational acceleration (9.80665 m/s² for Earth)
Unit for displaying the calculated height
Free Fall Height Results
Formula used: h = v₀t + ½gt²
Input values: Time: 0.00s, Initial velocity: 0m/s, Gravity: 9.80665m/s²
Height in meters: 0.0000 m
Physics Analysis
Example Calculations
Ball Drop (10 seconds)
Given: t = 10s, v₀ = 0 m/s, g = 9.80665 m/s²
Formula: h = ½gt²
Calculation: h = ½ × 9.80665 × 10²
Result: h = 490.33 m
Object with Initial Velocity
Given: t = 5s, v₀ = 10 m/s, g = 9.80665 m/s²
Formula: h = v₀t + ½gt²
Calculation: h = 10×5 + ½×9.80665×5²
Result: h = 172.58 m
Moon Gravity Example
Given: t = 10s, v₀ = 0 m/s, g = 1.625 m/s²
Formula: h = ½gt²
Calculation: h = ½ × 1.625 × 10²
Result: h = 81.25 m
Free Fall Height Equations
Height from Time
h = v₀t + ½gt²
When fall time is known
Height from Velocity
h = (v² - v₀²) / (2g)
When final velocity is known
Maximum Height
h_max = v₀² / (2g)
For upward initial velocity
Time to Maximum Height
t_max = v₀ / g
Time to reach peak height
Height References
Common height references for perspective:
Safety & Real World
This calculator assumes vacuum conditions (no air resistance)
Real objects experience terminal velocity due to air resistance
This is for educational purposes only - never attempt dangerous falls
Heights above 100m require consideration of air resistance effects
Understanding Free Fall Height
What is Free Fall Height?
Free fall height is the maximum vertical distance an object travels when falling under the influence of gravity alone. It depends on the object's initial velocity, fall time, and the gravitational acceleration of the celestial body.
Key Principles
- •Height increases quadratically with time (h ∝ t²)
- •Initial velocity affects the total height achieved
- •Different celestial bodies have different gravity values
- •Air resistance is ignored in ideal free fall calculations
Formula Breakdown
Basic Height Formula
h = v₀t + ½gt²
• h = height (meters)
• v₀ = initial velocity (m/s)
• t = time (seconds)
• g = gravitational acceleration (m/s²)
Energy Method
h = (v² - v₀²) / (2g)
Derived from conservation of energy
Useful when final velocity is known
Practical Applications
- ✓Physics Education: Understanding kinematics and gravity
- ✓Engineering: Designing safety systems and structures
- ✓Sports: Analyzing jumping and diving performance
- ✓Space Exploration: Planning landings on different planets
Real-World Limitations
- ⚠️Air Resistance: Becomes significant at high velocities
- ⚠️Terminal Velocity: Objects reach maximum speed due to drag
- ⚠️Altitude Effects: Gravity and air density change with height
- ⚠️Object Shape: Affects aerodynamic properties