Voltage at a Point in Time

Calculates an AC voltage at a specific point in time

Calculate Voltage at Time

Instantaneous Value Calculator

On this page you can calculate the instantaneous value of a sine wave at a specific point in time. The voltage can be entered as RMS or peak value.

V
Results
RMS voltage:
Peak voltage:
Instantaneous voltage:

Sine Wave Instantaneous Values

Sine wave instantaneous values

Instantaneous values of a sine wave at different times

Characteristic values
α = 0° u = 0V
α = 90° u = û (Maximum)
α = 180° u = 0V
α = 270° u = -û (Minimum)
α = 360° u = 0V
Parameters
\(\displaystyle û\) = Peak voltage [V]
\(\displaystyle u\) = Instantaneous voltage [V]
\(\displaystyle f\) = Frequency [Hz]
\(\displaystyle t\) = Time [s]
\(\displaystyle \omega\) = Angular frequency [rad/s]

Formulas for Calculating the Instantaneous Value

Basic formulas for sine waves

Angular frequency
\[\omega = 2\pi f\]

The angular frequency links frequency with the angle.

Instantaneous voltage
\[u(t) = û \cdot \sin(\omega t)\]

Voltage at a specific time t.

Complete formula
\[u(t) = û \cdot \sin(2\pi f \cdot t)\]

Direct relationship between frequency, time, and instantaneous voltage.

Important note

Radian mode: The calculator must be set to radian mode for formula calculation. For calculations in degrees use: \(u = û \cdot \sin\left(2\pi f \cdot t \cdot \frac{180}{\pi}\right)\)

Example calculations

Practical calculation examples

Example 1: Mains voltage after 5ms

Given: Urms = 230V, f = 50Hz, t = 5ms

\[û = 230V \times \sqrt{2} = 325.3V\]
\[\omega = 2\pi \times 50Hz = 314.16 \text{ rad/s}\]
\[u(5ms) = 325.3V \times \sin(314.16 \times 0.005) = 325.3V \times \sin(1.571) = 325.3V\]
Instantaneous voltage equals the peak voltage (90° position)
Example 2: Audio signal at 1kHz

Given: û = 1V, f = 1kHz, t = 0.25ms

\[\omega = 2\pi \times 1000Hz = 6283.2 \text{ rad/s}\]
\[u(0.25ms) = 1V \times \sin(6283.2 \times 0.00025) = 1V \times \sin(1.571) = 1V\]
90° position in the audio oscillation
Example 3: High frequency signal

Given: û = 5V, f = 1MHz, t = 125ns

\[\omega = 2\pi \times 10^6Hz = 6.283 \times 10^6 \text{ rad/s}\]
\[u(125ns) = 5V \times \sin(6.283 \times 10^6 \times 125 \times 10^{-9}) = 5V \times \sin(0.785) = 3.54V\]
45° position at high frequency
Important times in the sine wave
Zero crossings:
t = 0: u = 0V
t = T/2: u = 0V
t = T: u = 0V
Maxima:
t = T/4: u = +û
t = 3T/4: u = -û
ωt = π/2: Maximum
Slopes:
t = 0: max. slope
t = T/4: slope = 0
t = T/2: max. slope
Phase:
0°: ωt = 0
90°: ωt = π/2
180°: ωt = π

Theory of Instantaneous Values

Basics of Instantaneous Value Calculation

The voltage value at a specific point in time can be calculated or measured in various ways, depending on the type of system. Usually, this refers to the electrical voltage in a circuit at a given moment. To determine the voltage value at a specific time, you need to know the mathematical description of the voltage.

Sinusoidal AC voltages

If it is a sinusoidal AC voltage, the following equation can be used. With the help of the angular frequency formulas, the instantaneous value of voltage and current can be determined after a certain time t.

For voltages
\[u(t) = û \cdot \sin(\omega t)\]
\[u(t) = û \cdot \sin(2\pi f t)\]
For currents
\[i(t) = î \cdot \sin(\omega t)\]
\[i(t) = î \cdot \sin(2\pi f t)\]

Conversion between degrees and radians

If you want to calculate in degrees, you must convert the parameter for sin to degrees:

Conversion to degrees
\[u = û \cdot \sin\left(2\pi f \cdot t \cdot \frac{180}{\pi}\right)\]

Multiply the argument by 180/π for degree calculation.

Practical applications

Measurement technology
  • Oscilloscope measurements
  • Sample value determination
  • Signal analysis
  • Phase measurements
Electronics
  • ADC sampling
  • PWM generation
  • Synchronization
  • Triggering
Simulation
  • SPICE models
  • Time domain analysis
  • Transient calculation
  • Signal generation

Design notes

Practical considerations
  • Sampling theorem: Sampling rate at least 2× higher than the highest signal frequency
  • Phase relationships: Time shifts affect instantaneous values
  • Harmonics: Real signals often contain harmonics
  • Noise: Interference is superimposed on the useful signal
  • Drift: Observe frequency and amplitude stability
  • Trigger: Accurate time references required for measurements
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AC functions

Alternating voltage values  •  Alternating voltage and time  •  Frequency and wavelength  •  Alternating voltage value and angle  •  Frequency and periodic time  •  RMS value of a sinusoidal oscillation  •  RMS value of a sinusoidal oscillation with offset  •  RMS value of a sine pulse (half-wave rectification)  •  RMS value of a sine pulse (full-wave rectification)  •  RMS value of a square wave voltage  •  RMS value of a square pulse  •  RMS value of a triangle voltage  •  RMS value of a triangular pulse  •  RMS value of a sawtooth voltage  •  RMS value of a sawtooth pulse  •