Standard Score Calculator
Calculate the standard score (z-score) for any value. Find out how it compares to the mean and what percentile it falls in.
✓ Standard score (z-score)
✓ Percentile rank
✓ Above/below probabilities
Z-Score calculator
Compute the standard score and cumulative probability.
84.1% of the distribution falls below this value.
Understanding Standard Scores
A standard score (also called a z-score or standardized score) is a universal metric that lets you compare values from completely different scales. Whether you're comparing test scores, heights, or financial returns, standard scores put everything on the same playing field.
Standard Score to Percentile Table
z = -3.0: 0.1th percentile (bottom 0.1%)
z = -2.0: 2.3rd percentile
z = -1.0: 15.9th percentile
z = 0.0: 50th percentile (exactly average)
z = 1.0: 84.1st percentile
z = 2.0: 97.7th percentile
z = 3.0: 99.9th percentile (top 0.1%)
Comparing Across Different Scales
Who did better: SAT 1350 or ACT 30?
SAT: mean = 1060, SD = 217 → z = (1350-1060)/217 = 1.34
ACT: mean = 21, SD = 5.8 → z = (30-21)/5.8 = 1.55
ACT 30 is relatively stronger (higher z-score)
The 68-95-99.7 Rule
- 68% of data falls within ±1 standard deviation (z between -1 and 1)
- 95% of data falls within ±2 standard deviations
- 99.7% of data falls within ±3 standard deviations
📊 Other Standard Score Scales
Many tests use transformed standard scores: T-scores (mean 50, SD 10), stanines (1–9 scale), and scaled scores (SAT uses mean 500, SD 100 per section). All are derived from the z-score by linear transformation.