How do you calculate the peak voltage of a sine wave?

To calculate the peak voltage of a sine wave, you use the relationship between the root mean square (RMS) value and the peak value. For a sine wave, the peak voltage is equal to the RMS voltage multiplied by the square root of 2, which is approximately 1.414. This formula arises from the mathematical properties of sine waves, specifically how the RMS value represents an effective voltage that can produce the same power as the peak voltage in a resistive load.

The peak voltage gives you the highest voltage level reached by the sine wave, whereas the RMS value provides a measure of the continuous equivalent voltage in terms of the power produced. Therefore, using the RMS value and multiplying it by 1.414 accurately converts it to peak voltage for sinusoidal signals. This relationship is fundamental in electrical engineering, particularly when analyzing alternating current (AC) voltages.