Calculate velocity, mass, or potential energy from two known values using E=0.5mv² with unit conversions for energy, mass, and velocity.
Theoretical Velocity Formula
The theoretical velocity from a height is based on free fall under gravity, assuming no air resistance and no energy losses. The calculator uses standard gravity, g = 9.80665 m/s².
v = \sqrt{2gh}h = \frac{v^2}{2g}- v = theoretical velocity
- h = height or vertical drop
- g = acceleration due to gravity, 9.80665 m/s²
If you enter height, the calculator solves for theoretical velocity using v = √(2gh). If you enter velocity, it rearranges the same relationship to solve for height using h = v² / (2g).
Inputs are converted to base metric units before the calculation. Height is converted to meters, and velocity is converted to meters per second. The result is then converted back to the unit you selected.
Common Height and Theoretical Velocity Values
These values use standard gravity and ignore air resistance.
| Height | Theoretical Velocity | Approx. Velocity |
|---|---|---|
| 1 m | 4.43 m/s | 15.95 km/h |
| 5 m | 9.90 m/s | 35.64 km/h |
| 10 m | 14.00 m/s | 50.42 km/h |
| 25 m | 22.14 m/s | 79.72 km/h |
| 50 m | 31.32 m/s | 112.76 km/h |
Unit Conversions Used
| Quantity | Unit | Conversion to Base Unit |
|---|---|---|
| Height | ft | 1 ft = 0.3048 m |
| Height | in | 1 in = 0.0254 m |
| Velocity | ft/s | 1 ft/s = 0.3048 m/s |
| Velocity | km/h | 1 km/h = 0.277778 m/s |
Example Calculations
Example 1: Find theoretical velocity from height
You drop an object from a height of 10 m. Find its theoretical velocity just before impact.
v = \sqrt{2(9.80665)(10)}v = 14.0047\text{ m/s}The theoretical velocity is approximately 14.0047 m/s.
Example 2: Find height from theoretical velocity
An object has a theoretical velocity of 20 m/s. Find the height needed to reach that velocity under gravity.
h = \frac{20^2}{2(9.80665)}h = 20.3943\text{ m}The required height is approximately 20.3943 m.
FAQ
What does theoretical velocity mean?
Theoretical velocity is the speed predicted by a physics formula under ideal conditions. For this calculator, that means the object falls under gravity with no air resistance, drag, friction, or other losses.
Why is air resistance ignored?
The formula comes from conservation of energy for ideal free fall. Air resistance depends on object shape, size, mass, surface area, and air density, so it is not included in this basic theoretical calculation. Real falling objects often move slower than the theoretical value.
Can height or velocity be zero?
A zero height gives a zero theoretical velocity, and a zero velocity gives a zero height in the formula. The calculator requires a nonzero input because it is designed to solve for the missing value from one entered value.
