Sine Wave Calculator: Amplitude, Frequency, and Phase Explained

The sine wave is the fundamental building block of periodic signals. Every complex periodic signal — sound, light, radio waves, AC electrical current — can be decomposed into a sum of sine waves (Fourier analysis). Understanding the parameters that describe a sine wave is the foundation of signal processing, acoustics, and electronics.

The General Form

y(t) = A × sin(2πft + φ)

Where:

• A = Amplitude (peak value)
• f = Frequency in Hz (cycles per second)
• t = Time
• φ (phi) = Phase shift (horizontal offset in radians)
• 2πf = Angular frequency ω (omega), in radians per second

What Each Parameter Does

Amplitude: how tall the wave is. Doubles the amplitude = doubles the peak value = increases power by 4× (power is proportional to amplitude²). In audio: amplitude corresponds to loudness.

Frequency: how many complete cycles per second. Middle C on a piano: 261.63 Hz. A440 (standard tuning A): 440 Hz. Doubling frequency raises pitch by one octave.

Period: T = 1/f. How long one complete cycle takes. A 440 Hz sine wave has a period of 1/440 ≈ 2.27 milliseconds.

Phase shift: horizontal offset of the wave. Two sine waves with the same frequency but opposite phase (180° apart) cancel each other out — this is how noise-canceling headphones work.

AC Electricity

US household current is a sine wave: 120V RMS (root mean square) at 60 Hz. The actual peak voltage is 120 × √2 ≈ 170V. RMS is the effective voltage for power calculations.

European standard: 230V RMS at 50 Hz.

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This article is for informational purposes only. See our disclaimer.