Estimate speed, mass, or released potential energy using E = ½mv². Select a solve mode and enter the displayed known values. The model assumes rest initially and complete conversion to translational kinetic energy, with no losses. Height-based free-fall solves are also available.
Theoretical Velocity Formula
The theoretical velocity from a height is based on free fall under gravity, assuming no air resistance and no energy losses. For the height-based modes, the calculator uses standard gravity, g = 9.80665 m/s².
- v = theoretical velocity
- h = height or vertical drop
- g = acceleration due to gravity, 9.80665 m/s²
In the height-based modes, entering height solves for theoretical speed 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. Results show SI units with the other supported equivalents.
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 | 15.94 km/h |
| 5 m | 9.90 m/s | 35.65 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 | 112.74 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.
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.
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 the height-based modes, that means a vertical drop from rest with no air resistance, drag, friction, or other losses. The energy modes use released potential energy E and E = ½mv² under the same conversion assumptions.
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. Zero released energy or height gives zero speed for positive mass. Mass must be positive; solving for mass requires nonzero speed and positive energy. Zero energy and zero speed do not determine a unique mass.
