Z Score Calculator

Fill in three boxes, click Calculate. This z score calculator gives exact answers instantly, right on the page.

• Value (x) — the number you want to standardize, such as your test score of 85
• Mean (μ) — the average of the whole group, such as 72
• Standard deviation (σ) — how spread out the group is, such as 8

You immediately get two results: your z-score (how many standard deviations you are from the mean) and your percentile (the percentage of values below yours).

This page is more than a static z score calculator — it is also an AI tutor you can ask questions. The question box under the form takes full questions, photos of the problem, and follow-ups:

• Ask in plain words. “My class average is 72, the SD is 8, and I scored 85 — what is my percentile?” The AI reads it, fills the three boxes, and runs this z score calculator for you.
• Take a photo of your homework. No typing: the AI reads the numbers and fills the z score calculator form.
• Ask about the ideas, not just the number. “Why divide by the standard deviation?” or “What does a negative z-score tell me?” The AI explains step by step — every number still comes from the z score calculator on this page, so nothing is guessed.
• Work backwards, then keep asking. Give a z-score and ask for the raw value — this z score calculator covers both directions. Follow-up questions are welcome, so ask “why?” as often as you need: the z score calculator page keeps teaching.

You scored 85 on a test. Is that good? The number alone says nothing - the class averaged 72, and scores spread about 8 points either way. A z-score turns the raw 85 into a position: how far from the middle of the pack are you?

Measured in standard deviations - that is the unit a z score calculator reports. That one number is exactly what a z score calculator computes for you.

Read the picture: the pile of scores centers on 72. Your 85 is not "85 points good". It sits 13 points right of center - here that is about 1.6 standard deviations above the mean.

Every z-score reads the same way:

• z = 2: two standard deviations above the mean - well ahead of the pack.
• z = $-1.5$: one and a half below it - behind most of the class.
• z = 0: exactly average - the z score calculator reads zero, and you sit mid-pack.

Use this z score calculator to skip the arithmetic entirely.

Now the symbols. Three numbers go into every z score calculator, and the formula just restates the picture:

$z = \dfrac{x - \mu}{\sigma}$

Try these numbers in the z score calculator above — it confirms z = 1.625 instantly.

Scores are normally distributed. The mean is 72. The standard deviation is 8. You scored 85. Find your z-score.

1. Subtract the mean: $85 - 72 = 13$.
2. Divide by the standard deviation: $13 \div 8$.
3. So $z = 1.625 \approx 1.63$.

What it means: your score sits 1.63 SDs above average. A z-table puts that at about the 95th percentile. You beat roughly 95% of the class. Type the same three numbers into the z score calculator above - it walks these three steps with you.

The z score calculator above can do this reverse step for you: describe the problem in the AI box.

The z score calculator removes the arithmetic, but these habits still trip people up:

Sometimes you know the z-score and want the raw score.

A distribution has mean 100 and SD 15. A value sits at $z = -1.5$. Find the value.

1. Rearrange the formula: $x = \mu + z\sigma$.
2. Substitute: $x = 100 + (-1.5)(15)$.
3. So $x = 77.5$.

Negative z is not an error. The z score calculator keeps the sign - it only means below the mean.

1. Dividing by the variance. The denominator is the standard deviation, not its square.
2. Reading a negative z as wrong. Negative means below average - nothing more.
3. Mixing up direction. Value above the mean gives a positive z. Value below gives a negative one.

Check the sign before you check the number - the z score calculator above keeps it for you.