Formula Used
The calculator uses the general sine wave model:
y = A × sin(2πft + φ) + D
Here, A is amplitude, f is frequency, t is time, φ is phase in radians, and D is vertical shift.
Extra results use these related formulas:
Period = 1 / fAngular frequency = 2πfMaximum = D + |A|Minimum = D - |A|Peak to peak = 2|A|RMS of AC part = |A| / √2
How to Use This Calculator
- Enter the amplitude. This sets the height from the center line.
- Enter frequency in hertz. Use values greater than zero.
- Enter phase in degrees. The page converts it into radians.
- Enter vertical shift if the center line is not zero.
- Set the evaluation time for one exact wave value.
- Set a start time, end time, and sample count.
- Press Calculate to see the result above the form.
- Use CSV or PDF buttons to save the current calculation.
Example Data Table
| Amplitude |
Frequency |
Phase |
Shift |
Time |
Expected Value |
| 2 |
1 Hz |
0° |
0 |
0.25 s |
2 |
| 5 |
0.5 Hz |
30° |
1 |
1 s |
-1.5 |
| 10 |
60 Hz |
0° |
0 |
0.004167 s |
10 |
| 3 |
2 Hz |
90° |
4 |
0 s |
7 |
About This Sine Wave Formula Calculator
A sine wave describes smooth repeating motion. It appears in sound, alternating current, vibration, tides, and many school problems. This calculator turns the main sine model into clear numbers. You enter amplitude, frequency, phase, shift, and time. The tool returns the wave value, period, angular frequency, crest, trough, peak to peak distance, and root mean square estimate. It also builds sample points for a selected time range. These points help you copy data into charts or reports.
Why The Formula Matters
The general model is y equals A times sine of two pi f t plus phi, plus D. Amplitude A controls height from the center line. Frequency f controls cycles per second. Time t selects the point being measured. Phase phi moves the wave left or right. Shift D moves the entire wave up or down. When these parts are shown together, the shape becomes easier to read. A small phase change can move every crest. A large amplitude can double the peak to peak value. A higher frequency shortens the period.
Useful Results
The calculator reports several linked values. Period is one divided by frequency. Angular frequency is two pi times frequency. Maximum value equals shift plus absolute amplitude. Minimum value equals shift minus absolute amplitude. Peak to peak is twice the absolute amplitude. RMS is useful for pure alternating components. It equals amplitude divided by the square root of two. The sample table uses the same equation for each time step. This gives a quick view of the full wave behavior.
Reading The Wave
A positive value sits above the center line. A negative value sits below it. Zero crossings show balance points. Repeating samples reveal one cycle, many cycles, or only part of a cycle.
Practical Use Cases
Students can test trigonometry homework. Technicians can estimate signal behavior. Audio users can compare tones. Electrical learners can review alternating voltage. Physics users can model oscillation. The export buttons save the calculated summary and sample points. The CSV file works with spreadsheets. The PDF file gives a compact record for notes. Always confirm units before using results. Use hertz for frequency. Use seconds for time. Use degrees for phase in this page.
FAQs
What is a sine wave?
A sine wave is a smooth repeating curve. It models cycles in sound, voltage, motion, and many natural patterns. Its shape is controlled by amplitude, frequency, phase, and vertical shift.
What does amplitude mean?
Amplitude is the distance from the center line to a crest or trough. A larger amplitude makes the wave taller. It also increases the peak to peak value.
How is period calculated?
Period is calculated as one divided by frequency. If frequency is 2 Hz, the period is 0.5 seconds. It shows how long one complete cycle takes.
What is phase shift?
Phase shift moves the wave along the time axis. This calculator accepts phase in degrees, converts it into radians, and reports the matching horizontal shift in seconds.
What does vertical shift do?
Vertical shift moves the whole wave up or down. It changes the center line. It also changes the maximum and minimum values by the same amount.
Why use sample points?
Sample points show calculated wave values across a time range. They help you make charts, inspect cycles, and export signal data for later comparison.
Can this calculator handle negative amplitude?
Yes. A negative amplitude flips the sine wave across its center line. The calculator still reports maximum, minimum, and peak to peak values using absolute amplitude.
What units should I use?
Use hertz for frequency, seconds for time, and degrees for phase. Amplitude and shift can use any matching unit, such as volts, meters, or pressure units.