Z-plasty
An educational model for surgeons and trainees, not medical advice. It treats skin as flat and inextensible, so every value is the most the geometry allows. Lengthening in living tissue is typically less. It has not been clinically validated, and it should be used to compare candidate designs, not to predict the result of a specific operation.
60.0°/60.0° with 2.00 cm limbs lengthens the axis by 1.46 cm (73.2%)
Total incision 6.00 cm. Expansion penalty none.
Absolute lengthening
1.46 cm
Percent lengthening
73.2%
Axis length, cm
2.00 → 3.46
Expansion ratio E
1.732
- Flap with tip α
- Flap with tip β
- Central axis (lesion line)
- Incision or final scar
AB and CD are perpendicular here (cos α + cos β = 1), so 1/E equals the narrowing across the axis. In other designs it only relates the two diagonals.
How to read this drawing
Both panels share one scale. Letters follow the skin, so A and B stay the lesion ends and the A–B distance grows to E·L, while the final central scar C–D is L long. The flaps move rigidly between the first and last frames, but the frames in between are illustrative. The surrounding skin is not modelled, and it would have to stretch and shift to accommodate the flaps.
Tip-angle map
Percent lengthening for every α, β pair. Click or drag to move the design.
The dot marks the current design.
All outputs for this design
| Expansion ratio E | 1.732 |
|---|---|
| Percent lengthening | 73.21% |
| Absolute lengthening | 1.46 cm |
| Conjugate-diagonal ratio 1/E | 0.577 |
| Mean tip angle m | 60.0° |
| Angular imbalance d | 0.0° |
| Expansion penalty | 0.00 pp |
| Total incision length 3L | 6.00 cm |
| Lengthening per unit incision | 0.244 |
| Flap area, α / β | 1.73 / 1.73 cm² |
| Flap base width, α / β | 2.00 / 2.00 cm |
| Angle between AB and CD | 90.0° |
Ways to reach 1.46 cm of lengthening
Select a design to use it.
| Design | Lengthening | Limb L (cm) | Incision 3L (cm) | Area per flap (cm²) | Per unit incision |
|---|---|---|---|---|---|
| 23.9% | 6.12 | 18.35 | 9.36 | 0.08 | |
| 47.4% | 3.09 | 9.27 | 3.38 | 0.16 | |
| 73.2% | 2.00 | 6.00 | 1.73 | 0.24 | |
| 99.1% | 1.48 | 4.43 | 1.05 | 0.33 | |
| 123.6% | 1.18 | 3.55 | 0.70 | 0.41 |
† Outside 20–70°, where the manuscript notes clinical usefulness may be limited. Larger angles need less incision and flap area, but produce wider flaps that may need more tissue mobility.
What each variable does
Holding the others at the current design. The dot marks where you are.
How it is calculated
For tip angles α and β and limb length L:
- Expansion ratio: E = √((sin α + sin β)² + (1 − cos α − cos β)²)
- Percent lengthening: 100(E − 1)
- Absolute lengthening: L(E − 1)
- Conjugate-diagonal ratio: 1/E
- Total incision length: 3L
- Flap area: ½L² sin θ, for each tip angle θ
- Mean tip angle: m = (α + β)/2. Angular imbalance: d = |α − β|/2
- Expansion penalty: the percentage points lost compared with the symmetric design at the same m
Source: Daulat S, Moodley V, Ruta M, Nyström Å, Champagne LP. Geometric Factors of Central-Axis Lengthening in Two-Flap Z-Plasty. Unpublished manuscript, not yet peer reviewed.