To find the 'Effective Voltage' and the 'Average Voltage' of a voltage over time we have the following functions:

$$V_{eff}=\sqrt{\frac{1}{T}\int_{0}^{T} f(t)^2 \text{d}t}$$ $$V_{av}=\frac{1}{T}\int_{0}^{T} f(t) \text{d}t$$

But in my case it is impossible to find a general function for my voltage so can I use the surfaces? And if I can how can I find the 'Effective Voltage' and the 'Average Voltage'?

Thanks in advance

  • \$\begingroup\$ Why can't you find a general function? \$\endgroup\$
    – MathieuL
    Aug 27, 2015 at 17:18
  • \$\begingroup\$ What is f(t)? Because those formula apply to periodic function \$\endgroup\$
    – MathieuL
    Aug 27, 2015 at 17:19
  • \$\begingroup\$ It is a combination of 4 different functions, it is periodic \$\endgroup\$ Aug 27, 2015 at 17:19
  • \$\begingroup\$ What functions? \$\endgroup\$
    – MathieuL
    Aug 27, 2015 at 17:20
  • \$\begingroup\$ Do them individually to find the RMS of each then add the RMS of each up as per \$\sqrt{A^2+B^2 + ...}\$ \$\endgroup\$
    – Andy aka
    Aug 27, 2015 at 17:20

1 Answer 1


As you might know the definition of the definite integral \$\int_{a}^{b} f(x)dx\$ in layman's terms is area under the curve (and above the horizontal axis).

So, yes you could approximate the average value by just manualy calculating the area under the curve. But effective value contains \$f(x)^2dx\$, so you would first have to square the curve to get a new one and then calculate that area.

If the reason you cant solve the integral is that it is too complex you can use one of the online calculators, such as WolframAlpha or Symbolab to calculate it for you.


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