Sine Wave Calculator

Calculator Inputs

Provide any one of: frequency, period, or angular frequency. The calculator derives the others and generates a time-series table.

Wave type

Amplitude (A)

Non-negative. Peak-to-peak is 2A.

Vertical offset (D)

Shifts the wave up or down.

Frequency (f) in Hz

If set, overrides T and ω.

Period (T) in seconds

Used if f is empty and ω is empty.

Angular frequency (ω) in rad/s

Used if f is empty; otherwise derived.

Phase unit

Phase (φ)

Positive shifts left (in angle).

Time start (t0)

Time end (t1)

Time step (dt)

Smaller dt gives smoother sampling.

Time unit label

Output unit label

Decimal precision

Affects table and exports.

Reset

Example Data Table

Example: A=2, f=0.5 Hz, φ=0°, D=1, sampled from t=0 to 2 with dt=0.5.

t (s)	y	Notes
0.0	1.0000	sin(0)=0 → y=D
0.5	3.0000	sin(π/2)=1 → peak
1.0	1.0000	sin(π)=0 → back to offset
1.5	-1.0000	sin(3π/2)=-1 → trough
2.0	1.0000	sin(2π)=0 → cycle complete

Formula Used

The generated waveform follows: y(t) = A · sin(ωt + φ) + D or, for cosine mode: y(t) = A · cos(ωt + φ) + D

A is amplitude (half the peak-to-peak value).
f is frequency in hertz, T = 1/f.
ω is angular frequency, ω = 2πf.
φ is phase shift (degrees or radians).
D is vertical offset (DC component).

How to Use This Calculator

Choose sine or cosine.
Enter amplitude and vertical offset.
Fill either frequency, period, or angular frequency.
Set phase and its unit, if needed.
Select a time range and step for sampling.
Press Calculate to view stats and sample points.
Use CSV or PDF export for reporting or plotting.

FAQs

1) What is amplitude in a sine wave?

Amplitude A is the distance from the midline to a peak. The full peak-to-peak height is 2A. If A is 0, the signal becomes a flat line at the offset D.

2) How do frequency and period relate?

Frequency f counts cycles per second. Period T is the time for one cycle. They are reciprocals: T = 1/f. This tool computes both from whichever one you provide.

3) What does phase shift change?

Phase φ shifts the waveform along the time axis in angular terms. A positive φ moves the pattern earlier in time for the same t. Use degrees for convenience or radians for direct formulas.

4) Why use angular frequency ω?

Angular frequency ω simplifies calculus and physics formulas. It links to frequency by ω = 2πf. Many models in vibrations, AC analysis, and wave equations use ω directly.

5) What is RMS and why is it shown?

RMS measures the effective magnitude of a varying signal. For a pure sine centered at zero, RMS equals A/√2. With a vertical offset, RMS increases because the DC component adds energy.

6) How should I pick a time step dt?

Use a step small enough to capture curvature. A common choice is 50–200 samples per period. Very small dt can create huge tables, so the calculator limits the maximum number of points.

7) Why do my values look constant?

This often happens when dt is too large relative to the period, or when amplitude A is near zero. Reduce dt, increase the time range, and confirm you entered one valid value among f, T, or ω.