# Miles Equation

The miles equation is a simplified method of calculating the response of a single degree of freedom system to a random vibration base input, where the input is in the form of a power spectral density. The g^{2}/hz is the unit of PSD measurement of an operating hard disk drive. Here is the online calculator for g^{2}/hz to grms conversion using Miles Equation. Using this equation, you can calculate grms, with the formula √[(pi / 2) (F x Q x P)] and by multiplying grms by 3 gives you X_{peak}.

## G^2/HZ to Grms Conversion

The miles equation is a simplified method of calculating the response of a single degree of freedom system to a random vibration base input, where the input is in the form of a power spectral density. The g^{2}/hz is the unit of PSD measurement of an operating hard disk drive. Here is the online calculator for g^{2}/hz to grms conversion using Miles Equation. Using this equation, you can calculate grms, with the formula √[(pi / 2) (F x Q x P)] and by multiplying grms by 3 gives you X_{peak}.

Code to add this calci to your website

#### Formula:

X_{grms} = √[(Π / 2) F x Q x P]
X_{peak} = 3 X_{grms}
**Where,**
F = Frequency
P = Acceleration
Q = Quality Factor
### Example:

Calculate X_{grms} and X_{peak} for frequency of 2 Hz, quality factor of 5 and accelration of 7 g^{2}/Hz.

#### Solution:

X_{grms} = √[(Π / 2) F x Q x P]

= √[ (3.14 / 2) 2 x 5 x 7]

= 10.486 g

X_{peak} = 3 X_{grms}

= 3 x 10.486

= 31.4579 g