Method
z=(x−μ)/σ. Under a standard-normal model, the left-tail percentile is Φ(z) and the right tail is 1−Φ(z).
Math worksheet
Z-Score and Normal Percentile Calculator
Standardize a raw score, recover its model-based percentile and inspect both normal-tail probabilities.
The calculation runs locally. Exact-integer tools avoid floating point; decimal and transcendental tools report rounding limits.
Method and verification guide
How the Z-Score and Normal Percentile Calculator works
z=(x−μ)/σ. Under a standard-normal model, the left-tail percentile is Φ(z) and the right tail is 1−Φ(z). The calculator keeps the intermediate values visible so you can reproduce the answer independently.
Interpret the result
The z-score is signed distance from the mean measured in standard-deviation units.
Check the assumptions
Turning a z-score into a percentile assumes a normal distribution; it is not an empirical rank in the entered population.
Local calculation
Everything runs in this browser. Inputs are not sent to an external calculator.
Rounding
Displayed values may be rounded for readability while calculations use full floating-point precision unless the tool explicitly uses exact integers.
Scope
Turning a z-score into a percentile assumes a normal distribution; it is not an empirical rank in the entered population.
Simple by design
Three steps to a clearer number.
Enter your details
Use realistic values in each field. You can change them anytime.
Calculate instantly
The formula runs locally, so there is no account or waiting time.
Use the result
Treat the answer as a practical estimate for your next decision.