Complex Modulus Calculator

This complex modulus calculator works out the modulus, or magnitude, of any complex number written in the form a + bi, along with its argument, the two figures you need to convert a complex number into polar form. Complex numbers underpin electrical engineering, signal processing, control theory and pure maths, and the modulus is simply the complex-number equivalent of absolute value: it tells you how far the point (a, b) sits from the origin on the complex plane. To use it, enter the real part, labelled a, and the imaginary part, labelled b, using positive or negative values as needed. The calculator instantly returns the modulus as its main result, plus the argument shown two ways, in degrees and in radians, so you can use whichever unit your course or software expects. Under the hood it applies Pythagoras, taking the square root of a squared plus b squared for the modulus, and the atan2 function on b and a for the argument, which keeps the angle in the correct quadrant. The worked example on this page, 3 + 4i, shows a modulus of 5 and an argument of about 53.13 degrees, a useful check that you are reading your own numbers correctly. Results are rounded for display, so treat many decimal places as illustrative precision rather than guaranteed accuracy for extreme inputs.

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