Calculate impact velocity, time, and distance for falling objects.
Drop Height (Distance)
Fall Time (Duration)
Standard Earth gravity is approx 9.81 m/s²
Calculation Results
Velocity at Impact:0 m/s
Velocity (km/h):0 km/h
Total Fall Time:0 s
Total Fall Distance:0 m
*Calculations assume a vacuum (no air resistance).
Understanding Free Fall and Fall Rate
In physics, free fall is any motion of a body where gravity is the only force acting upon it.
This Fall Rate Calculator helps you determine how fast an object is traveling (velocity) and how long it takes to reach the ground based on the height from which it was dropped.
These calculations assume the object is falling in a vacuum, meaning air resistance (drag) is not factored into the final speed.
The Formulas
The calculator uses the standard kinematic equations for constant acceleration. Here, $g$ represents gravitational acceleration (typically 9.81 m/s² on Earth).
1. Calculating by Height
If you know the distance an object falls ($h$), you can find the time ($t$) and impact velocity ($v$):
Time to Impact: t = √(2h / g)
Velocity at Impact: v = √(2gh)
2. Calculating by Time
If you know how long the object has been falling ($t$), you can find the distance ($h$) and velocity ($v$):
Distance Fallen: h = 0.5 * g * t²
Velocity: v = g * t
How to Use This Calculator
Select Calculation Mode: Choose whether you know the Drop Height (in meters) or the Fall Time (in seconds).
Enter Values: Input the known value. For example, if dropping a stone from a bridge, input the bridge height.
Check Gravity: The default is set to Earth's standard gravity (9.80665 m/s²). You can adjust this for other celestial bodies (e.g., Moon = 1.62 m/s², Mars = 3.71 m/s²).
Calculate: Click the button to see the impact velocity in both meters per second (m/s) and kilometers per hour (km/h).
Common Gravity Values (m/s²)
Earth: 9.81 m/s²
Moon: 1.62 m/s²
Mars: 3.71 m/s²
Jupiter: 24.79 m/s²
Frequently Asked Questions
Does mass affect the fall rate?
In a vacuum (as calculated here), no. A feather and a hammer will hit the ground at the same time if there is no air resistance. However, in the real world, air resistance affects lighter objects with high surface areas more significantly.
What is terminal velocity?
Terminal velocity is the maximum constant speed that a falling object will eventually reach when the resistance of the medium (air) prevents further acceleration. This calculator determines velocity before terminal velocity is reached or assumes a vacuum where terminal velocity doesn't exist.
function toggleInputs() {
var mode = document.getElementById('calculationMode').value;
var heightGroup = document.getElementById('heightInputGroup');
var timeGroup = document.getElementById('timeInputGroup');
if (mode === 'height') {
heightGroup.style.display = 'block';
timeGroup.style.display = 'none';
} else {
heightGroup.style.display = 'none';
timeGroup.style.display = 'block';
}
// Hide results when mode switches to avoid confusion
document.getElementById('results').style.display = 'none';
}
function calculateFallRate() {
var mode = document.getElementById('calculationMode').value;
var g = parseFloat(document.getElementById('gravity').value);
// Validate Gravity
if (isNaN(g) || g <= 0) {
alert("Please enter a valid positive number for Gravity.");
return;
}
var velocity = 0;
var time = 0;
var distance = 0;
if (mode === 'height') {
var h = parseFloat(document.getElementById('dropHeight').value);
if (isNaN(h) || h < 0) {
alert("Please enter a valid height.");
return;
}
distance = h;
// t = sqrt(2h/g)
time = Math.sqrt((2 * h) / g);
// v = sqrt(2gh)
velocity = Math.sqrt(2 * g * h);
} else {
var t = parseFloat(document.getElementById('fallTime').value);
if (isNaN(t) || t < 0) {
alert("Please enter a valid time.");
return;
}
time = t;
// h = 0.5 * g * t^2
distance = 0.5 * g * t * t;
// v = g * t
velocity = g * t;
}
// Convert velocity to km/h for readability
var velocityKmh = velocity * 3.6;
// Display Results
document.getElementById('results').style.display = 'block';
document.getElementById('resVelocity').innerHTML = velocity.toFixed(2) + " m/s";
document.getElementById('resVelocityKmh').innerHTML = velocityKmh.toFixed(2) + " km/h";
document.getElementById('resTime').innerHTML = time.toFixed(2) + " s";
document.getElementById('resDistance').innerHTML = distance.toFixed(2) + " m";
}