Z-Score Calculator
Standard score, percentile and tail probabilities.
Enter your values
Enter the value (x) you are working with.
Enter the mean (μ) you are working with.
Enter the standard deviation (σ) you are working with.
Results update instantly as you type — no submit needed. Your values are remembered on this device, and the shareable link reopens the calculator with exactly these numbers.
- Z-score
- 2.1333
- Percentile
- 98.36%
- Probability above this value
- 1.645%
- Two-tailed p-value
- 3.2897%
Working
- 1z = (132 − 100) ÷ 15 = 2.1333
Quick answer
A z-score is how many standard deviations a value sits from the mean: z = (x − μ) ÷ σ.
z = (x − μ) ÷ σ
At a glance
| What it does | Standard score, percentile and tail probabilities. |
|---|---|
| Category | Statistics |
| Inputs needed | Value (x), Mean (μ), Standard deviation (σ) |
| Main output | Z-score |
| Formula | z = (x − μ) ÷ σ |
| Cost | Free — no sign-up, no download |
How to use the Z-Score Calculator
- 1Enter the raw value.
- 2Add the population mean and standard deviation.
- 3Read the z-score and percentile.
Inputs explained
- Value (x)
- Enter the value (x) you are working with.
- Mean (μ)
- Enter the mean (μ) you are working with.
- Standard deviation (σ)
- Enter the standard deviation (σ) you are working with.
Worked example
Using the values the calculator loads with:
Inputs
- Value (x)132
- Mean (μ)100
- Standard deviation (σ)15
Results
- Z-score2.1333
- Percentile98.36%
- Probability above this value1.645%
- Two-tailed p-value3.2897%
- z = (132 − 100) ÷ 15 = 2.1333
Frequently asked questions
What z-score is significant?
At the conventional 5% two-tailed level, |z| above 1.96 is significant; 2.58 corresponds to the 1% level.
Can a z-score be negative?
Yes — it simply means the value sits below the mean.
What do I need to enter into the Z-Score Calculator?
Just 3 values: value (x), mean (μ), standard deviation (σ). Every field starts with a realistic example, so you can change one number at a time and watch the result update instantly.
How does the Z-Score Calculator work out the answer?
A z-score is how many standard deviations a value sits from the mean: z = (x − μ) ÷ σ. It applies the formula z = (x − μ) ÷ σ and shows the working so you can check each step by hand.
Is the Z-Score Calculator free, and do I need an account?
It is completely free with no sign-up, no download and no usage limit. Everything is calculated in your browser, so the numbers you type never leave your device.
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.