Calculate theoretical velocity from height or find the height needed for a given velocity using gravity and metric or imperial units.
Theoretical Velocity Formula
The calculator estimates ideal free-fall speed from a vertical drop height, or reverses that calculation. It assumes an object starts from rest, constant standard gravity g = 9.80665 m/s², and no air resistance.
- v = nonnegative theoretical speed
- h = nonnegative vertical drop height
- g = standard gravity, 9.80665 m/s²
Choose Theoretical speed from height or Drop height from speed, enter the known quantity and select a result unit. Changing an input unit converts its existing value; changing the result unit takes effect on the next Calculate.
Velocity Unit Conversion Factors
The calculator supports meters per second, kilometers per hour, miles per hour, and feet per second.
| Unit | Convert to m/s | Convert from m/s |
|---|---|---|
| m/s | multiply by 1 | multiply by 1 |
| km/h | divide by 3.6 | multiply by 3.6 |
| mph | multiply by 0.44704 | divide by 0.44704 |
| ft/s | multiply by 0.3048 | divide by 0.3048 |
Height and Theoretical Velocity Relationship
| Known Value | Formula to Use | Meaning |
|---|---|---|
| Drop height | v = √(2gh) | Finds ideal speed after a vertical fall from rest. |
| Theoretical speed | h = v² ÷ (2g) | Finds the ideal drop height needed for a speed. |
Example Problems
Example 1: Find speed from drop height
Suppose the vertical drop height is 10 m.
The theoretical speed is approximately 14.00474919 m/s.
Example 2: Find drop height from speed
Suppose the theoretical speed is 10 m/s.
The ideal drop height is approximately 5.09858106 m.
FAQ
What does theoretical velocity mean here?
Here it means the speed magnitude predicted by ideal free fall from rest. Direction is not inferred from a signed velocity input.
Does the estimate include air resistance?
No. Drag, buoyancy and altitude-dependent gravity are omitted. This constant-gravity model is unsuitable for long drops or terminal-speed predictions.
Can I enter zero height or zero speed?
Yes. Zero drop height corresponds to zero speed for an object starting from rest. Negative height and speed are outside this magnitude-based model.
