Fixed-Point Q-Format Converter

About this calculator

Q-format (Qm.n notation) represents a real number as a fixed-point integer by reserving n bits for the fractional part: the stored raw integer equals the real value multiplied by 2ⁿ, so a Q15 (Q1.15) value in a 16-bit word has a resolution of 1/2¹⁵ ≈ 0.0000305 and a range of roughly −1 to 0.99997. Converting a real number to Q-format means rounding value × 2ⁿ to the nearest integer, which introduces quantization error equal to the difference between that rounded integer (scaled back) and the original value.

Embedded-systems and DSP (digital signal processing) engineers use Q-format on microcontrollers and DSP chips without a hardware floating-point unit — common in audio codecs, motor-control firmware, and older ARM Cortex-M and TI TMS320 designs — because fixed-point arithmetic runs faster and more predictably than software-emulated floating point. This calculator converts either direction and reports the resolution and rounding error so firmware developers can judge whether a given bit width is precise enough for their signal chain.