Mixed dentition analysis: Tanaka-Johnston and Moyers explained

Simplified Orthodontics Academy · Published 26 October 2026

Key points

In the mixed dentition, the permanent canines and premolars are not yet in the mouth, so their widths cannot be measured. A mixed dentition analysis estimates them.
Both methods here start from one measurement: the sum of the widths of the four lower permanent incisors.
Tanaka-Johnston uses prediction equations: half the incisor sum plus 11.0 mm in the upper arch, or plus 10.5 mm in the lower arch, for one side.
Moyers reads the estimate from tables, separate for males and females, at a chosen probability level.
The results are estimated widths, not measurements. How well they fit varies between populations.

What a mixed dentition analysis is for

A space analysis compares two lengths in each arch: the space available, and the space the teeth need. In the permanent dentition both can be measured on the model. In the mixed dentition one part is missing. The permanent canine and the two premolars on each side are still unerupted, so the space they will need is unknown.

A mixed dentition analysis fills that gap with an estimate. The lower permanent incisors erupt early, so they can be measured while the canines and premolars are still developing. Their summed width is used to estimate the summed width of the canine and two premolars on one side.

Figure 1. The lower arch drawn straight, with FDI tooth numbers. The incisors (solid) are measured; the canine and premolars on each side (dashed) are estimated from them. The same lower incisor sum is used for the upper arch.

Tanaka-Johnston prediction equations

Tanaka and Johnston calculated linear regression equations for the widths of unerupted canines and premolars in a large sample of orthodontic patients. They reported that their equations were broadly similar to the Michigan mixed dentition analysis. They also gave a simple approximation of comparable accuracy [1]:

Upper canine + premolars, one side = (sum of the 4 lower incisors ÷ 2) + 11.0 mm

Lower canine + premolars, one side = (sum of the 4 lower incisors ÷ 2) + 10.5 mm

The upper estimate also starts from the lower incisors, not the upper ones. The method needs no table and no radiograph.

Moyers probability tables

The Moyers method also starts from the sum of the four lower incisors. Instead of an equation, the estimate is read from a table [2]. There are separate tables for the upper and lower arch and for males and females. Each table gives several probability levels; 50%, 75% and 95% are the ones used in Simplified Cast.

A higher level gives a larger estimate, so the real teeth are less likely to be wider than it. Simplified Cast uses 75% unless another level is chosen. Table 1 shows the 75% values for some incisor sums, next to the Tanaka-Johnston estimates for the same sums.

Table 1. Estimated width of the canine and two premolars on one side, in millimetres
Lower incisor sum	Tanaka-Johnston upper	Tanaka-Johnston lower	Moyers 75% female upper	Moyers 75% female lower	Moyers 75% male upper	Moyers 75% male lower
21.0	21.5	21.0	20.8	20.3	21.0	21.0
22.0	22.0	21.5	21.0	20.8	21.5	21.4
23.0	22.5	22.0	21.3	21.3	22.0	21.9
24.0	23.0	22.5	21.6	21.9	22.5	22.3
25.0	23.5	23.0	21.9	22.4	23.0	22.8

Table 1. Estimated widths in millimetres, one side. The Moyers values are those of the tables built into Simplified Cast, which cover lower incisor sums from 19.5 to 25.5 mm in steps of 0.5 mm. Between two rows, Cast and the calculator below read the value on a straight line. The two methods give different figures for the same incisors.

From estimated widths to a space analysis

The estimate is one part of the space analysis for each arch. The space needed is the sum of the four incisors of that arch plus the estimated canine and premolars on both sides. It is compared with the space available, the arch perimeter measured between the first molars.

Space discrepancy = space available − (sum of the 4 incisors of that arch + 2 × estimated width for one side)

A positive result means more space than the estimated tooth widths need; a negative result means less. This is the calculation Simplified Cast shows for each method once the incisor widths and the arch perimeter are in.

Worked example

These widths are invented for this example; they are not from a patient. All values are in millimetres.

Lower incisor	42	41	31	32
Width	6.0	5.4	5.5	6.1

Sum of the four lower incisors: 6.0 + 5.4 + 5.5 + 6.1 = 23.0 mm.
Tanaka-Johnston, upper: 23.0 ÷ 2 + 11.0 = 22.5 mm per side. Lower: 23.0 ÷ 2 + 10.5 = 22.0 mm per side.
Moyers 75%, female: 21.3 mm upper and 21.3 mm lower per side. Male: 22.0 mm upper and 21.9 mm lower per side.
Space analysis for the lower arch, with an invented arch perimeter of 66.0 mm. With Tanaka-Johnston: 66.0 − (23.0 + 2 × 22.0) = −1.0 mm. With Moyers 75% for a male: 66.0 − (23.0 + 2 × 21.9) = −0.8 mm. For a female: 66.0 − (23.0 + 2 × 21.3) = +0.4 mm.

The same incisors give a small shortage with one method and a small surplus with another. So a result means little without the method and, for Moyers, the probability level. The calculator below gives the same figures; choose “Fill the worked example” to see them.

Limits of the estimates

They are estimates. The real canines and premolars can be wider or narrower. A single figure hides that spread; the Moyers probability levels make it visible.
Populations differ. Both methods were derived in other populations, and studies in other groups have found systematic differences. In 670 Syrian patients, the Tanaka-Johnston equations tended to overestimate the real widths in both males and females. The Moyers 75% values were close to the real widths in males but overestimated them in females, and the authors found the Moyers method the more accurate of the two in their sample [3]. In another Syrian sample of 600 patients, Nourallah and colleagues derived new regression equations and tables for their population [4].
Sex matters for Moyers. The female and male tables differ. If the sex is not recorded, Simplified Cast shows both.
Outside the table. The Moyers tables used here stop at incisor sums of 19.5 and 25.5 mm. Beyond them, Cast and the calculator continue the last straight line and show a warning, so treat those values with extra caution.
Measurement error. An error of 1 mm in the incisor sum changes each Tanaka-Johnston estimate by 0.5 mm, and the lower space discrepancy by 2 mm: 1 mm in the incisors themselves and 0.5 mm for each side.

Tanaka-Johnston and Moyers calculator

Do this in Simplified Cast

Simplified Cast runs the mixed dentition space analysis (Tanaka-Johnston, Moyers) and shows the estimated widths of the unerupted canines and premolars. It measures the incisors on the 3D study model, or takes caliper widths you type. The analysis is in the Free plan.

Open Simplified Cast About Simplified Cast

Educational content for clinicians and students. Estimated widths and reference values vary between populations. This page does not replace clinical judgement.

References

Tanaka MM, Johnston LE. The prediction of the size of unerupted canines and premolars in a contemporary orthodontic population. J Am Dent Assoc. 1974;88(4):798-801. doi: 10.14219/jada.archive.1974.0158. PMID: 4525402
Moyers RE. Handbook of Orthodontics. 4th ed. Chicago: Year Book Medical Publishers; 1988.
Burhan AS, Nawaya FR. Prediction of unerupted canines and premolars in a Syrian sample. Prog Orthod. 2014;15:4. doi: 10.1186/2196-1042-15-4. PMID: 24393608
Nourallah AW, et al. New regression equations for predicting the size of unerupted canines and premolars in a contemporary population. Angle Orthod. 2002;72(3):216-221. doi: 10.1043/0003-3219(2002)072<0216:NREFPT>2.0.CO;2. PMID: 12071605