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Home/ Questions/Q 1010547
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Editorial Team
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Editorial Team
Asked: May 16, 20262026-05-16T09:05:58+00:00 2026-05-16T09:05:58+00:00

Is there a clever/efficient algorithm for determining the hypotenuse of an angle (i.e. sqrt(a²

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Is there a clever/efficient algorithm for determining the hypotenuse of an angle (i.e. sqrt(a² + b²)), using fixed point math on an embedded processor without hardware multiply?

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  1. Editorial Team
    Editorial Team
    2026-05-16T09:05:59+00:00Added an answer on May 16, 2026 at 9:05 am

    Unless you’re doing this at >1kHz, multiply even on a MCU without hardware MUL isn’t terrible. What’s much worse is the sqrt. I would try to modify my application so it doesn’t need to calculate it at all.

    Standard libraries would probably be best if you actually need it, but you could look at using Newton’s method as a possible alternative. It would require several multiply/divide cycles to perform, however.

    AVR resources

    • Atmel App note AVR200: Multiply and Divide Routines (pdf)
    • This sqrt function on AVR Freaks forum
    • Another AVR Freaks post
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