Calculate theoretical velocity from height or find the height needed for a given velocity using gravity and metric or imperial units.
Root Mean Square Velocity Formula
The calculator uses the RMS-to-peak relationship for a sinusoidal velocity waveform. For a sine wave, the root mean square velocity is the peak velocity multiplied by 0.7071, which is approximately the same as dividing by the square root of 2.
V_rms = V_peak * 0.7071
V_peak = V_rms / 0.7071
- V_rms = root mean square velocity
- V_peak = peak velocity
- 0.7071 = approximate value of 1 / sqrt(2)
If you enter peak velocity, the calculator multiplies it by 0.7071 to find RMS velocity. If you enter RMS velocity, it divides by 0.7071 to find peak velocity. When you select different units, the value is converted to meters per second for the calculation, then converted back to your selected output unit.
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 | multiply by 0.277778 | multiply by 3.6 |
| mph | multiply by 0.44704 | multiply by 2.23694 |
| ft/s | multiply by 0.3048 | multiply by 3.28084 |
Peak and RMS Velocity Relationship
| Known Value | Formula to Use | Meaning |
|---|---|---|
| Peak velocity | V_rms = V_peak × 0.7071 | Finds the effective velocity of a sinusoidal motion. |
| RMS velocity | V_peak = V_rms ÷ 0.7071 | Finds the maximum velocity from the RMS value. |
Example Problems
Example 1: Find RMS velocity from peak velocity
Suppose the peak velocity is 12 m/s.
V_rms = 12 * 0.7071
V_rms = 8.4852 m/s
The root mean square velocity is 8.4852 m/s.
Example 2: Find peak velocity from RMS velocity
Suppose the RMS velocity is 30 km/h.
V_peak = 30 / 0.7071
V_peak = 42.4268 km/h
The peak velocity is 42.4268 km/h.
FAQ
What does root mean square velocity mean?
Root mean square velocity is an effective velocity value. For a sinusoidal motion, it represents the constant velocity that would have the same average squared effect as the changing velocity over one cycle.
Why is RMS velocity lower than peak velocity?
For a sine wave, the velocity is only at its peak instantaneously. Most of the cycle is spent below the peak value, so the RMS value is lower. The RMS value is about 70.71% of the peak value.
Is this the same as RMS speed in gas laws?
No. This calculator uses the sinusoidal relationship between peak velocity and RMS velocity. RMS speed in kinetic theory uses a different formula, commonly based on temperature, molar mass, and the gas constant.
