Standard scores and percentiles on one bell curve

By the IEP Atlas editorial teamLast updated November 1, 2026

Short answer

On a test with a mean of 100 and a standard deviation of 15, a standard score of 85 is about the 16th percentile, 90 is the 25th, 100 is the 50th, 110 is the 75th and 115 is the 84th. Every norm-referenced score type maps onto the same bell curve, so you can convert between them with the chart below.

Evaluation reports mix score types. One page shows standard scores, the next shows scaled scores, and the behavior section uses T scores. They all describe the same thing: how far a student's performance sits from the average of a norm group, in standard deviation units. Once you can place each one on the bell curve, a report reads much faster.

The chart on this page comes from the math of the normal curve. It is not taken from any test's norm tables. A test's own manual is still the authority for that test's scores, confidence intervals and descriptive labels.

Standard score to percentile chart

The rows run in steps of 5 standard score points, which is one third of a standard deviation. Percentiles are rounded.

Standard score (mean 100, SD 15)	z score	Scaled score (mean 10, SD 3)	T score (mean 50, SD 10)	Percentile rank
145	+3.00	19	80	99.9
140	+2.67	18	77	99.6
135	+2.33	17	73	99
130	+2.00	16	70	98
125	+1.67	15	67	95
120	+1.33	14	63	91
115	+1.00	13	60	84
110	+0.67	12	57	75
105	+0.33	11	53	63
100	0.00	10	50	50
95	-0.33	9	47	37
90	-0.67	8	43	25
85	-1.00	7	40	16
80	-1.33	6	37	9
75	-1.67	5	33	5
70	-2.00	4	30	2
65	-2.33	3	27	1
60	-2.67	2	23	0.4
55	-3.00	1	20	0.1

To convert any score yourself: z = (score minus the mean) divided by the SD. Then multiply z by the new SD and add the new mean. A scaled score of 7 gives z = (7 minus 10) / 3 = -1.00, which is a standard score of 100 + (-1.00 × 15) = 85.

How the bell curve works

On a normal curve, about 68% of scores fall within one standard deviation of the mean, which is 85 to 115 for standard scores. About 95% fall within two, which is 70 to 130. About 99.7% fall within three, from 55 to 145. These proportions are a property of the curve itself, and they are why 85 and 115 show up so often as the edges of the average range.

Standard scores are equal-interval. A 5-point gap means the same distance anywhere on the scale. Percentile ranks are not. Moving from 100 to 105 jumps 13 percentile points (50th to 63rd), while moving from 70 to 75 jumps only 3 (2nd to 5th). Scores bunch up in the middle of the curve, so small changes there look large in percentiles.

That is why you should never average percentiles or subtract them to show growth. Use standard scores for any arithmetic, then convert back if a parent wants a percentile.

Reading T scores on behavior scales

On most achievement and cognitive tests, a higher score is better. On many behavior and emotional rating scales, a higher T score means more of the problem behavior. A T score of 70 on an attention scale is two standard deviations above the mean, at about the 98th percentile, and usually signals a concern. Some scales flip this for adaptive or strength scales, where low scores signal concern. Check the direction in the report before you explain it.

Confidence intervals

Every score has measurement error. Reports show it as a confidence interval, built from the test's standard error of measurement (SEM). A 90% interval is roughly the score plus or minus 1.65 SEM. With an SEM of 3 points, a score of 82 has a 90% interval of about 77 to 87.

Read the band, not the point. A score of 82 with a band of 77 to 87 overlaps the low end of the average range. Two scores whose bands overlap a lot may not be meaningfully different. The test manual sets the size of a difference that counts as significant; do not guess it from the chart.

One student's scores, worked through

Elena is a fictional fifth grader evaluated in February 2026 for reading and attention concerns. Her report showed these scores:

Measure	Score as reported	Standard score equivalent	Percentile
Verbal reasoning composite	Standard score 104	104	61
Working memory subtest	Scaled score 6	80	9
Basic reading (word reading and decoding)	Standard score 79	79	8
Reading comprehension	Standard score 86 (90% band 81 to 91)	86	18
Math calculation	Standard score 97	97	42
Teacher rating, inattention scale	T score 68	127	96 (higher means more concern)

Put on one curve, the picture is clear. Verbal reasoning and math sit in the average range. Basic reading is about 1.4 SD below the mean, and working memory about 1.3 SD below. Comprehension is closer to average than decoding, which fits a student whose understanding is stronger than her word reading. The teacher's attention rating is high, near the 96th percentile for concern.

The team used the pattern, not one number, to plan instruction: explicit decoding work, reduced working memory load in directions and a check on attention at home. The psychoeducational report recommendations page shows how findings like these become recommendations. To turn them into present levels, see evaluation results to present levels.

Scores and eligibility rules: where states differ

Federal rules require a variety of assessment tools and forbid using any single measure as the sole basis for eligibility.^[1] States set many of the numeric details.

Topic	Federal rule	Where states differ
Single score as the decision	Not allowed^[1]	All states follow this; how much weight scores carry varies
Specific learning disability	States may not require a severe discrepancy between ability and achievement and must permit a response to intervention process^[2]	Some states allow a discrepancy formula, some use a pattern of strengths and weaknesses, some rely on intervention data
Intellectual disability	Requires significantly below-average intellectual functioning with deficits in adaptive behavior^[3]	Cutoffs, often near two SDs below the mean, and how measurement error is applied vary
Developmental delay (young children)	States may use it for children ages 3 through 9 or a subset of that range^[3]	Many express delay in SDs or percent delay; the cutoffs and areas counted differ
Speech or language impairment	Defined by impact on educational performance^[3]	Some states name a score cutoff; others stress functional evidence
Descriptive labels ("low average," "below average")	Not addressed	Labels come from each test publisher and differ between tests

Check your state's eligibility rules before you use any number as a cutoff. The 13 categories of special education page covers the categories in plain words.

Explaining scores to parents

Lead with the standard score and the percentile together: "a standard score of 79, which is about the 8th percentile, meaning higher than about 8 of every 100 students her age."
Say what a percentile is not. It is not a percent correct.
Skip the grade equivalent. It is easy to misread and hard to defend.
Show the bell curve. One sketch with the student's scores marked does more than a page of numbers.

Parents reading a report on their own can use how to read a psychoeducational report. For which tests produce these scores, see what tests are in a psychoeducational evaluation. The glossary entry on norm-referenced tests explains where the norms come from. The full process is in the IEP evaluation process.

Frequently asked questions

What percentile is a standard score of 85?

About the 16th percentile, because 85 is one standard deviation below the mean of 100. The student scored higher than about 16 of every 100 students in the norm group.

What is the difference between a scaled score and a standard score?

Both are norm-referenced. Standard scores usually have a mean of 100 and an SD of 15. Scaled scores, common on subtests, have a mean of 10 and an SD of 3. A scaled score of 7 equals a standard score of 85.

Why do percentiles change so much near the middle?

Most scores cluster near the mean, so a few standard score points there pass many students. Near the tails, few students score, so the same few points move the percentile very little.

Use it in IEP Atlas

Sources

34 CFR §300.304: Evaluation procedures, U.S. Department of Education (IDEA website)
34 CFR §300.307: Specific learning disabilities, U.S. Department of Education (IDEA website)
34 CFR §300.8: Child with a disability, Legal Information Institute, Cornell Law School

Written and checked by the IEP Atlas editorial team under our editorial policy. This guide describes general practice and federal rules. It is not legal advice; your state may add requirements, and the IEP team makes the decisions for each student.