Enter the sine-wave peak amplitude (volts), frequency (Hz), and time (seconds) into the calculator to determine the instantaneous voltage V(t) for a sine wave (assumes zero phase shift and no DC offset). Frequency alone does not determine voltage.

Instantaneous Voltage & Frequency-to-Voltage (F-to-V) Calculator

Instantaneous V(t)
F-to-V Converter (IC)

Enter any 3 values to calculate the missing variable (note: solving for f or t is not unique because sine is periodic; this returns the principal solution).

Instantaneous Voltage (Sine Wave) Formula

The following formula is used to calculate the instantaneous voltage of a sine wave (assumes zero phase shift and no DC offset).

V = Va * sin ( 2*pi*f*t)
  • Where V is the instantaneous voltage at time t (volts)
  • Va is the peak amplitude of the sine wave (volts)
  • f is the frequency (Hz)
  • t is the time (seconds)

To calculate instantaneous voltage, multiply the peak amplitude by the sine of 2 times pi times the frequency times the time (with the sine argument in radians).

Instantaneous Voltage Table (A = 5.00 V, t = 0.25 ms; V = A × sin(2π f t))
Frequency (Hz) Voltage (V)
10.008
50.039
100.079
200.157
500.392
600.471
1000.782
2001.545
2501.913
4002.939
5003.536
6004.045
1,0005.000
1,2504.619
1,5003.536
2,0000.000
2,500-3.536
3,000-5.000
4,0000.000
5,0005.000
*Instantaneous voltage using V = A × sin(2π f t). Assumes amplitude A = 5.00 V and time t = 0.25 ms (0.00025 s). Results range from −A to +A.

How to Calculate Instantaneous Voltage?

The following example problems outline how to calculate instantaneous voltage for a sine wave using the formula above.

Example Problem #1

  1. First, determine the peak amplitude of the voltage (volts). In this example, the peak amplitude is determined to be 50.
  2. Next, determine the frequency (Hz). For this problem, the frequency is measured to be 60.
  3. Next, determine the time (seconds). In this case, the time is found to be 0.002.
  4. Finally, calculate the instantaneous voltage using the formula above: 

V = Va * sin ( 2*pi*f*t)

Inserting the values from above and solving yields: 

V = 50 * sin(2*π*60*0.002) = 34.2274 (volts)

Example Problem #2

Using the same method as above, determine the variables required by the formula. For this example problem, these are:

peak amplitude of the voltage (volts) = 30

frequency (Hz) = 6

time (seconds) = 0.05

Enter these given values into the calculator above yields: 

V = 30 * sin(2*π*6*0.05) = 28.5317 (volts)