Free tool · Binet–Stern–Terman formula
Mental Age Calculator
The original ratio IQ formula, as a working calculator. Enter any two of mental age, chronological age and IQ — the third is solved instantly, with the arithmetic shown. Useful for psychology coursework, for reading older literature, and for understanding what "mental age" meant before deviation IQ replaced it.
IQ = (mental age ÷ chronological age) × 100
Fill any two fields and the third updates as you type. Nothing is sent anywhere.
What is the mental age formula?
The mental age formula is the original ratio IQ equation: IQ = (mental age ÷ chronological age) × 100. Rearranged, mental age = (IQ × chronological age) ÷ 100, and chronological age = mental age ÷ (IQ ÷ 100). William Stern proposed the ratio in 1912; Lewis Terman added the ×100 multiplier in 1916 to remove the decimal point.
| To find | Formula | Worked example |
|---|---|---|
| Ratio IQ | (MA ÷ CA) × 100 | MA 12, CA 10 → (12 ÷ 10) × 100 = 120 |
| Mental age | (IQ × CA) ÷ 100 | IQ 120, CA 10 → (120 × 10) ÷ 100 = 12 years |
| Chronological age | MA ÷ (IQ ÷ 100) | MA 12, IQ 120 → 12 ÷ 1.2 = 10 years |
How to calculate mental age from IQ, step by step
Start with the ratio formula
IQ = (mental age ÷ chronological age) × 100. This is the equation Terman published in the 1916 Stanford revision of the Binet–Simon scale.
Rearrange it for mental age
Multiply both sides by chronological age, then divide by 100: mental age = (IQ × chronological age) ÷ 100.
Substitute your numbers
For a 10-year-old with a ratio IQ of 120: (120 × 10) ÷ 100 = 12. Their mental age is 12 years.
Read it correctly
A mental age of 12 means test performance matched that of a typical 12-year-old — not that the child is twelve in any other sense. And it only holds for children; see below.
Reference table: mental age by IQ and chronological age
Mental age in years, computed as (IQ × CA) ÷ 100. Included because it is the fastest way to see how the ratio formula behaves — and how quickly it becomes implausible as chronological age rises.
| Chronological age | IQ 70 | IQ 85 | IQ 100 | IQ 115 | IQ 130 |
|---|---|---|---|---|---|
| 5 | 3.5 | 4.3 | 5.0 | 5.8 | 6.5 |
| 8 | 5.6 | 6.8 | 8.0 | 9.2 | 10.4 |
| 10 | 7.0 | 8.5 | 10.0 | 11.5 | 13.0 |
| 12 | 8.4 | 10.2 | 12.0 | 13.8 | 15.6 |
| 16 | 11.2 | 13.6 | 16.0 | 18.4 | 20.8 |
| 30 | 21.0 | 25.5 | 30.0 | 34.5 | 39.0 |
| 50 | 35.0 | 42.5 | 50.0 | 57.5 | 65.0 |
Look at the last two rows. A 50-year-old with a ratio IQ of 130 would have a "mental age" of 65 — which is meaningless, because there is no sense in which a typical 65-year-old outperforms a typical 50-year-old on a cognitive battery. That is the failure the field had to fix.
Why the formula does not work for adults
Ratio IQ breaks down in adulthood because cognitive test performance rises steeply through childhood and then plateaus. Once it plateaus, dividing by an ever-increasing chronological age drags the quotient downward regardless of ability — a 40-year-old would score roughly half the ratio IQ of a 20-year-old of identical ability. Modern tests use deviation IQ instead.
Deviation IQ compares your raw performance to the distribution of scores among people in your own age band, expressed in standard-deviation units and normed to a mean of 100 with a standard deviation of 15. The Stanford–Binet adopted it in its 1960 revision, and every major modern instrument — the WAIS, the WISC, the Stanford–Binet 5 — uses it. No current clinical assessment reports a ratio IQ.
This calculator vs. the mental age test
These two tools share a phrase and nothing else. The calculator implements a historical arithmetic relationship. The mental age test is a self-report questionnaire about mindset and maturity that borrows the term loosely. You cannot feed a result from one into the other — there is no conversion, because they are not measuring the same kind of thing. The full explanation is on the psychology page.
Frequently asked questions
What is the mental age formula?
IQ = (mental age ÷ chronological age) × 100. Rearranged: mental age = (IQ × chronological age) ÷ 100, and chronological age = mental age ÷ (IQ ÷ 100). Stern proposed the ratio in 1912; Terman added the ×100 in 1916.
How do you calculate mental age from IQ?
Multiply the IQ score by the person's chronological age, then divide by 100. A 10-year-old with a ratio IQ of 120 has a mental age of (120 × 10) ÷ 100 = 12 years — their performance matched that of a typical 12-year-old.
Does the mental age formula work for adults?
No. Cognitive performance plateaus in adulthood while chronological age keeps rising, so the quotient falls with age regardless of ability. Modern IQ tests use deviation IQ, which compares you to the score distribution within your own age band.
Is ratio IQ still used today?
No. The Stanford–Binet moved to deviation IQ in 1960 and every major modern test followed. Ratio IQ is now of historical interest only — useful for understanding older literature, not for assessing anyone.
What is a normal mental age for a child?
By definition, a mental age equal to the child's chronological age, which produces a ratio IQ of 100. Mental age above chronological age means above-average performance for that age group; below means below-average. Interpreting a child's score meaningfully requires a qualified psychologist and a properly administered instrument, not a formula.
Can I use this to work out my mental age from an online IQ test?
You can put the numbers in, but the output will not mean much. Free online IQ tests are generally unnormed and inflate scores, and the ratio formula is invalid for adults in the first place. Two layers of unreliability do not combine into an answer.
Sources
- Britannica — Mental age
- Intelligence quotient — Stern's ratio, Terman's multiplier, and the shift to deviation IQ
- Stanford–Binet Intelligence Scales — 1916 revision and the 1960 deviation-IQ change