How do you get a p-value from a confidence interval?

Using the Altman–Bland method: estimate the standard error from the interval width (SE = (upper - lower) / (2 x z), where z matches the interval's confidence level), compute the test statistic z = estimate / SE, then p = 2 x (1 - Phi(|z|)). For ratios, do this on the natural-log scale.

How do you get a confidence interval from a p-value?

From the p-value, recover z = Phi-inverse(1 - p/2), then SE = |estimate| / z. The interval is estimate +/- z_conf x SE for a difference, or exp(ln(estimate) +/- z_conf x SE) for a ratio.

Does it work for odds ratios and hazard ratios?

Yes. Choose the ratio option and the tool works on the log scale, which is correct for odds ratios, risk ratios, and hazard ratios.

It assumes a normal (Wald) approximation and a symmetric interval on the appropriate scale, which is what most reported intervals use. It is intended for differences and log-ratios, not for proportions near 0 or 1 or very small samples.

Home › Tools › p-value ↔ Confidence Interval

Convert between p-values and confidence intervals

Turn a reported confidence interval into a p-value, or a p-value and estimate into a CI — for differences or ratios (OR, RR, HR). Uses the Altman–Bland method.

Direction

Measure

Confidence level of the interval

Point estimate

Lower limit

Upper limit

Point estimate

p-value

Result

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How the conversion works

A confidence interval and a p-value carry the same information about precision — they’re two views of an estimate and its standard error. The Altman–Bland method moves between them:

CI → p: recover the standard error from the interval width, SE = (upper − lower) / (2·z), then z = estimate / SE and p = 2·(1 − Φ(|z|)).
p → CI: recover z = Φ⁻¹(1 − p/2), then SE = |estimate| / z and CI = estimate ± z_conf·SE.
Ratios: for odds, risk, and hazard ratios the same steps run on the natural-log scale, then exponentiate back.

Assumes a normal (Wald) approximation and an interval that’s symmetric on the appropriate scale — true of most reported intervals. Not for proportions near 0/1 or very small samples.

Frequently asked questions

How do I get a p-value from a 95% CI?

SE = (upper − lower)/(2 × 1.96), then z = estimate/SE and p = 2 × (1 − Φ(|z|)). For ratios, use the log of each value first.

How do I get a CI from a p-value?

Recover z = Φ⁻¹(1 − p/2), set SE = |estimate|/z, then form estimate ± z_conf × SE (or exponentiate for a ratio).

Does it handle odds/hazard ratios?

Yes — pick “Ratio” and the tool works on the log scale, which is correct for OR, RR, and HR.

Why does p → CI need the estimate?

The p-value fixes the ratio estimate/SE but not the scale; the estimate pins down SE so the interval can be placed.

Does it store anything?

No. Everything runs in your browser; nothing is uploaded or saved.

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