Carey space analysis explained: space available vs space required
Key points
- A space analysis compares two lengths in one arch: the space available and the space the teeth need. The difference is the space discrepancy.
- In Carey’s analysis of the lower arch, the space required is the sum of the mesiodistal widths of the ten teeth from one second premolar to the other.
- The space available is the arch perimeter, from the mesial contact of one first molar to the mesial contact of the other.
- Simplified Cast measures the perimeter in four straight segments, from five points, unless another method is chosen.
- Discrepancy = space available − space required. A negative result means less space than the teeth need; a positive result means more.
What a space analysis compares
A space analysis asks one question: do the teeth fit in the arch? It answers it by comparing the space available in the arch with the space required by the teeth, and reporting the difference [1]. The analysis described here is named after Carey and is done on the lower arch.
This version uses the measured widths of all the teeth in front of the first molars, so those teeth must have erupted. When the permanent canines and premolars are still unerupted, their widths have to be estimated first; that is the job of a mixed dentition analysis.
Simplified Cast runs Carey’s analysis on the lower arch. It runs the same comparison on the upper arch, from one upper second premolar to the other, and calls it the arch perimeter analysis. The method below is the same for both; the examples use the lower arch.
Space required: the ten tooth widths
The space required is the sum of the mesiodistal widths of the ten teeth in front of the first molars. With FDI numbers, these are 45, 44, 43, 42, 41, 31, 32, 33, 34 and 35. Each width is the distance between the tooth’s mesial and distal contact points.
The first molars are not part of the sum. The space is measured up to their mesial surfaces, so both lengths in the analysis end at the same place.
In Simplified Cast you click the two contact points of each tooth on the 3D model, or type a width measured with a caliper. Either way, the space required is the same sum.
Space available: the arch perimeter in segments
The space available is the length of the arch, from the mesial contact point of the first molar on one side, over the contact points of the teeth in front of it, to the mesial contact point of the first molar on the other side. The arch is curved, so one straight caliper reading cannot measure it. One way around this is to split the arch into straight segments, measure each one and add them.
Simplified Cast does this, unless you choose otherwise, with four segments between five points (Figure 1):
- From the mesial contact of the right first molar to the distal contact of the right canine.
- From the distal contact of the right canine to the midline, the contact of the central incisors.
- From the midline to the distal contact of the left canine.
- From the distal contact of the left canine to the mesial contact of the left first molar.
Space available = segment 1 + segment 2 + segment 3 + segment 4
Cast also offers straight segments through as many points as you click, or a smooth curve through the points, like a brass wire laid along the arch. On an arch with even curves, a smooth curve gives a slightly longer perimeter than straight lines through the same points, because a straight line is the shortest path between two points. So the perimeter depends a little on the method as well as on the arch. When you compare two measurements, use the same method for both.
If you have measured the perimeter some other way, you can also type the total into Cast instead of placing the points.
The space discrepancy
Space discrepancy = space available − space required
This is the difference reported by a space analysis [1], and the one Simplified Cast shows.
- A negative result means the teeth need more space than the arch perimeter provides. This is often described as crowding.
- A positive result means the arch provides more space than the teeth need. This is often described as spacing.
- Zero means the two lengths are equal.
The number describes the arch at the level of the contact points. It does not say why the space is short or in excess, or what to do about it.
Worked example
These values are invented for this example; they are not from a patient. The tooth widths are the lower widths of the worked example in our Bolton article. All values are in millimetres.
| Tooth | 45 | 44 | 43 | 42 | 41 | 31 | 32 | 33 | 34 | 35 |
|---|---|---|---|---|---|---|---|---|---|---|
| Width | 7.2 | 7.0 | 6.9 | 6.0 | 5.4 | 5.5 | 6.1 | 6.9 | 7.1 | 7.3 |
| Perimeter segment | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
| Length | 14.0 | 17.6 | 17.9 | 14.3 |
- Space required: 7.2 + 7.0 + 6.9 + 6.0 + 5.4 + 5.5 + 6.1 + 6.9 + 7.1 + 7.3 = 65.4 mm.
- Space available: 14.0 + 17.6 + 17.9 + 14.3 = 63.8 mm.
- Space discrepancy: 63.8 − 65.4 = −1.6 mm.
The ten teeth need 1.6 mm more than the measured arch perimeter. If segment 4 had measured 17.0 mm instead of 14.3 mm, the space available would be 66.5 mm and the result +1.1 mm: a change in one segment turns a shortage into a surplus. The calculator below gives the same figures; choose “Fill the worked example” to see them.
Limits of the analysis
- Small errors add up. The result comes from ten widths and four segments. If every width is read 0.1 mm too large, the space required grows by 1.0 mm, and the discrepancy changes by the same amount.
- The perimeter depends on the points and the method. Where the five points are placed, and whether the perimeter is taken as straight segments or a curve, both change the space available.
- One number for the whole arch. The discrepancy does not say where in the arch the space is short. Simplified Cast’s segmental space analysis splits the comparison into six segments of each arch.
- Only the dental arch. The analysis does not include the curve of Spee, the incisor position or the jaw relationship. Simplified Cast has a separate discrepancy calculation that adds the curve of Spee and the incisor position.
- All ten teeth must be measurable. A missing, broken or unerupted tooth leaves a gap in the sum. For unerupted canines and premolars, an estimate replaces the measurement, as in the mixed dentition analysis.
This article describes the measurement only. What a given discrepancy means for a patient depends on the full clinical picture and is outside its scope.
Carey space analysis calculator
Do this in Simplified Cast
Simplified Cast compares space available against space required: the arch perimeter analysis on the upper arch, and Carey’s analysis on the lower. It measures 3D study models from STL, PLY or OBJ scans, or takes caliper widths you type. Both analyses are in the Free plan.
Educational content for clinicians and students. Measurements depend on the method and the examiner. This page does not replace clinical judgement.
References
- Correia GDC, Habib FAL, Vogel CJ. Tooth-size discrepancy: a comparison between manual and digital methods. Dental Press J Orthod. 2014;19(4):107-113. doi: 10.1590/2176-9451.19.4.107-113.oar