Standard Score Converter
Enter a score on any scale — z, T, IQ, NCE, scaled score, stanine, sten, percentile, or a raw score with its mean and SD — and see it on all the others, with the percentile rank, a normal curve showing where it falls and every formula worked out. Free, no sign-up, and nothing leaves your browser.
Enter a score to see it on every scale.
How to Use the Standard Score Converter
- 1. Pick the scale you have. Choose z, T, IQ-style, NCE, scaled, College Board, percentile, stanine or sten. If you only have a raw score, choose “Raw score” and enter the mean and standard deviation of the group it came from.
- 2. Enter the score. Percentile ranks must be above 0 and below 100; stanines are whole numbers from 1 to 9 and stens from 1 to 10.
- 3. Read every scale at once. The cards show z, the percentile rank, T, IQ, NCE and the stanine; the table adds the scaled score, the College Board score and the sten, with each scale's mean and SD.
- 4. Check the curve and the working. The bell curve shades everything below the score, and the formulas show how each conversion was made.
How Standard Scores Relate
A standard score says how many standard deviations a result sits from the mean. The z-score is the base: z = (x − mean) ÷ SD, with a mean of 0 and an SD of 1. Every other linear scale is just z restated with a different mean and SD, so converting between them is two steps — back to z, then forward to the new scale.
| Scale | Mean | SD | Formula | Where it is used |
|---|---|---|---|---|
| z-score | 0 | 1 | z | Statistics in general |
| T-score | 50 | 10 | 50 + 10z | Personality and behaviour inventories, many clinical measures (McCall, 1922) |
| Deviation IQ | 100 | 15 | 100 + 15z | Wechsler scales and the Stanford–Binet; some older tests used SD 16 |
| NCE | 50 | 21.06 | 50 + 21.06z | US Title I evaluation (Tallmadge and Wood, 1976) |
| Scaled score | 10 | 3 | 10 + 3z | Wechsler subtests |
| CEEB | 500 | 100 | 500 + 100z | The original College Board scale |
| Stanine | 5 | 2 | round(2z + 5), 1–9 | Educational reporting |
| Sten | 5.5 | 2 | round(2z + 5.5), 1–10 | Cattell's 16PF and other personality scales |
Modern SAT section scores are no longer centred exactly on 500, so treat the CEEB row as the classic scale rather than a conversion for today's SAT.
Percentile Ranks, Stanines and Stens
The percentile rank of a z-score is 100 × Φ(z), where Φ is the standard normal cumulative distribution. A z of 1 gives the 84.13th percentile, and a z of 2 gives the 97.72nd. This is only right if the scores really are normally distributed; with skewed scores, use the percentile ranks from the test's own norm table.
Stanines (“standard nines”) cut the normal curve into nine bands, each half a standard deviation wide except the open-ended first and last. The middle stanine, 5, covers z from −0.25 to 0.25 — the 40th to 60th percentile — and the nine bands hold roughly 4%, 7%, 12%, 17%, 20%, 17%, 12%, 7% and 4% of scores. Stens (“standard tens”) use ten bands with edges at whole and half standard deviations: sten 5 is z from −0.5 to 0 and sten 6 is z from 0 to 0.5. A stanine or sten stands for a band, not a point, so converting it back to z uses the middle of the band and is approximate.
Worked Examples
Click “Try an example” to convert an IQ of 115. Then z = (115 − 100) ÷ 15 = 1. The percentile rank is 84.13, so about 84% of scores fall below it. On the other scales: T = 50 + 10 × 1 = 60, NCE = 50 + 21.06 × 1 = 71.06, scaled score 13 and College Board 600. The stanine is round(2 × 1 + 5) = 7 and the sten is round(2 × 1 + 5.5) = 8.
Now “Try a raw score”: a student scores 82 on a test with a mean of 70 and a standard deviation of 8. Then z = (82 − 70) ÷ 8 = 1.5, which is the 93.32nd percentile. That is a T-score of 65, an IQ-style score of 122.5, an NCE of 81.59, a stanine of 8 and a sten of 9. The same procedure works for any raw score, as long as you use the mean and SD of the comparison group.
Frequently Asked Questions
- How do you convert a z-score to a T-score?
- Multiply the z-score by 10 and add 50: T = 50 + 10z. A z of 1.5 gives T = 65, and a z of −1 gives T = 40. To go the other way, z = (T − 50) ÷ 10.
- What percentile is an IQ of 130?
- On a scale with mean 100 and SD 15, an IQ of 130 is z = 2, which is the 97.72nd percentile if scores are normally distributed — about 2.3% of people score higher. An IQ of 115 is the 84th percentile and 85 is the 16th.
- What is an NCE score and why is the SD 21.06?
- A normal curve equivalent is a standard score with a mean of 50 and an SD of 21.06. That SD was chosen so that NCE values of 1, 50 and 99 coincide with the percentile ranks 1, 50 and 99, and because NCEs are equal-interval, unlike percentiles, they can be averaged. They are used mainly in US federal education evaluation.
- What is a stanine?
- A stanine (“standard nine”) is a score from 1 to 9 with a mean of 5 and an SD of 2, made by rounding 2z + 5. Stanine 5 holds the middle 20% of scores, 4–6 together hold about the middle 55%, and 1 and 9 each hold the extreme 4%.
- What is the difference between a stanine and a sten?
- A stanine has nine bands with a mean of 5 and is centred on z = 0, so the middle band straddles the mean. A sten has ten bands with a mean of 5.5 and the mean sits on the edge between sten 5 and sten 6. Stens are common in personality testing; stanines in school reports.
- Is a T-score of 60 good?
- It is one standard deviation above the average, the 84th percentile. Whether that is “good” depends on the test: on an achievement test it is above average, while on a symptom inventory it may mark the edge of clinical interest. Many inventories treat T-scores from 40 to 60 as the average range.
- What is the difference between a percentile and a percentage?
- A percentage is the share of items answered correctly, such as 41 out of 50. A percentile rank is the share of other people who scored lower, so a score at the 84th percentile beat about 84% of the comparison group, whatever the percentage correct was.