Functions to easily convert between number of sigma (standard deviations) and percent confidence intervals.

stdev_confidence_conversions.py

# see https://en.wikipedia.org/wiki/68–95–99.7_rule

import numpy as np
from scipy import special

def sigma_to_pct_conf(z: float) -> float:
    """If an uncertainty is ±zσ, what is the corresponding confidence interval?"""
    return special.erf(z/np.sqrt(2))

def pct_conf_to_sigma(conf: float) -> float:
    """If we have `conf`% confidence in our result, ± how many σ is that?"""
    return special.erfinv(conf)*np.sqrt(2)

if __name__ == "__main__":
    print(f"±1σ = {sigma_to_pct_conf(1):.2%} confidence")
    print(f"90% confidence = ±{pct_conf_to_sigma(0.9):.3f}σ")