A z-score (standard score) measures how many standard deviations a value is from the mean of a distribution. A z-score of 0 is exactly average; +1 is one SD above average (84th percentile).

A T-score is a scaled score with a mean of 50 and a standard deviation of 10. It avoids negative numbers and decimals. T = 50 + 10z.

How are stanines calculated?

Stanines (standard nines) run from 1 to 9 with a mean of 5 and SD of 2. They divide the normal curve into 9 bands: stanines 1–3 are below average, 4–6 average, and 7–9 above average.

What is an NCE score?

Normal Curve Equivalent (NCE) scores have a mean of 50 and SD of 21.06. Unlike percentiles, they are equal-interval, which makes them useful for statistical comparisons in educational research.

What is a standard score with mean 100 and SD 15?

This scale is used for IQ tests (Wechsler, Stanford-Binet). A score of 115 equals a z-score of +1 (84th percentile); 85 equals a z-score of -1 (16th percentile).

How do I convert a standard score to a percentile?

Turn the score into a z-score, z = (score − mean) ÷ SD, then look up the area of the normal curve below z: percentile = Φ(z) × 100. For a standard score of 85 (mean 100, SD 15), z = −1.00 and Φ(−1) = 0.159, so the percentile rank is 16. A score of 115 is the 84th percentile and 130 is the 98th (97.7).

What does a scaled score of 7 mean?

Subtest scaled scores (Wechsler, mean 10, SD 3) put 7 one standard deviation below the mean: z = −1.00, the 16th percentile, equal to a standard score of 85. Mapped onto the standard-score bands, scaled scores of 8–11 are average (90–105), 12–13 high average, 6–7 low average and 4–5 very low.

What are the current Wechsler descriptors?

WISC-V reports use 130+ Extremely High, 120–129 Very High, 110–119 High Average, 90–109 Average, 80–89 Low Average, 70–79 Very Low and 69 or below Extremely Low. Older reports used Very Superior, Superior and Borderline for the 130+, 120–129 and 70–79 bands.

What is a sten score?

A sten (standard ten) runs from 1 to 10 with a mean of 5.5 and SD of 2, so each sten is half a standard deviation wide. It is common on personality questionnaires such as the 16PF. Sten = 5.5 + 2z, rounded and kept within 1–10.

Why do percentile ranks and standard scores differ?

Percentile ranks are not equal-interval — the difference between the 50th and 60th percentile is smaller than between the 80th and 90th. Standard scores are equal-interval, making them better for arithmetic comparisons.

Standard Score Converter

Enter any standard score type, or a raw score with your own mean and SD, and convert to percentile rank, z-score, T-score, scaled score, stanine, sten and NCE.

Enter a Score

Score Type

Score Value

Classification Reference

Range	Percentile	Label (older label)
130+	≥ 98th	Extremely High (Very Superior)
120–129	91–97th	Very High (Superior)
110–119	75–90th	High Average
90–109	25–73rd	Average
80–89	9–23rd	Low Average
70–79	2–8th	Very Low (Borderline)
≤ 69	≤ 2nd	Extremely Low

Wechsler (WISC-V) descriptors on the standard score scale (mean=100, SD=15). The classification uses the standard-score equivalent of any input.

Enter a score and click Convert to see equivalents.

Standard score to percentile conversion chart

Normal-curve equivalents for standard scores (mean 100, SD 15) in steps of 5, about one third of an SD.

Standard score	z	Percentile	T	Scaled	Stanine	NCE	Descriptor
145	+3.00	99.9	80	19	9	99	Extremely High
140	+2.67	99.6	77	18	9	99	Extremely High
135	+2.33	99.0	73	17	9	99	Extremely High
130	+2.00	97.7	70	16	9	92	Extremely High
125	+1.67	95.2	67	15	8	85	Very High
120	+1.33	90.9	63	14	8	78	Very High
115	+1.00	84.1	60	13	7	71	High Average
110	+0.67	74.8	57	12	6	64	High Average
105	+0.33	63.1	53	11	6	57	Average
100	0.00	50.0	50	10	5	50	Average
95	-0.33	36.9	47	9	4	43	Average
90	-0.67	25.2	43	8	4	36	Average
85	-1.00	15.9	40	7	3	29	Low Average
80	-1.33	9.1	37	6	2	22	Low Average
75	-1.67	4.8	33	5	2	15	Very Low
70	-2.00	2.3	30	4	1	8	Very Low
65	-2.33	1.0	27	3	1	1	Extremely Low
60	-2.67	0.4	23	2	1	1	Extremely Low
55	-3.00	0.1	20	1	1	1	Extremely Low

Percentile = Φ(z) × 100, the share of the norm group scoring below. NCE is limited to 1–99 by definition. Test publishers' norm tables can differ by a point because they are built from real samples rather than the ideal curve.

Score scales and formulas

Scale	Mean	SD	From z
Standard score / IQ	100	15	100 + 15z
T-score	50	10	50 + 10z
Scaled score	10	3	10 + 3z
Stanine	5	2	round(5 + 2z), 1–9
Sten	5.5	2	round(5.5 + 2z), 1–10
NCE	50	21.06	50 + 21.06z
Stanford-Binet (old)	100	16	100 + 16z

Worked examples

T-score 65 to percentile: z = (65 − 50) ÷ 10 = 1.50; Φ(1.5) = 0.933, so the 93rd percentile, standard score 122.5.
Scaled score 7: z = (7 − 10) ÷ 3 = −1.00, the 16th percentile, standard score 85, Low Average.
Raw score with your own norms: a class test with mean 72 and SD 8; a score of 84 gives z = 1.50, the 93rd percentile, T = 65.
Stanine 7: the band from z = +0.75 to +1.25, the 77th to 89th percentiles. Converting a stanine uses its midpoint, z = +1.00.

Summary

Enter any standard score type, or a raw score with your own mean and SD, and convert to percentile rank, z-score, T-score, scaled score, stanine, sten and NCE.

How it works

Select the score type you want to convert from (e.g., z-score, T-score, IQ, scaled score, stanine, sten, NCE, or percentile), or choose Custom to enter a raw score with your own mean and standard deviation.
Enter your score value in the input field.
The tool calculates the equivalent z-score using the known mean and standard deviation for that scale.
The normal distribution CDF converts the z-score to a percentile rank.
All equivalent score types are displayed simultaneously in the results panel.

Use cases

Interpret standardized test results from school psychologist reports.
Compare scores across different assessment instruments (e.g., IQ vs. achievement tests).
Understand where a student falls relative to peers using percentile rank.
Convert z-scores from research data into more intuitive T-scores or stanines.
Explain assessment results to parents or students in plain terms.
Cross-reference scores from different norm-referenced tests in IEP meetings.

Frequently Asked Questions

Last updated: 2026-10-09 · Reviewed by Nham Vu