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Bust Dart Rotation Calculator

A dart is a fold of paper about its point, so it can be handled as an angle. With a 5 cm intake as the chord and 12 cm to the apex as the radius, that is 2 × asin(2.5 ÷ 12) = 24.0°. The angle does not change wherever you move it: close the side dart and open a waist dart, or move it to the shoulder or the neckline, and the same 24.0° travels. With 30 cm from apex to hem, rotating the dart swings the hem open by 0.42 rad × 30 = 12.6 cm.

Your numbers

Rotation angle

24°

Hem swing

12.6cm

Formula

Rotation angle = 2 × asin(Intake per dart ÷ 2 ÷ Dart leg to the apex), Hem swing = Rotation angle × π ÷ 180 × Apex to hem

The same angle means different intakes at different lengths — 24.0° taken 6 cm from the apex is only 2.5 cm. So copying "a 5 cm dart" to another position doubles the angle and makes the bust point out like a cone. Stop the dart point 1.5–2 cm short of the bust point rather than on it, or you build that cone deliberately. Past about 30° a single dart cannot swallow the shaping: split it into two side by side, or convert to a princess seam. Actually rotating the paper is always more reliable than the arithmetic.

What to enter

InputDefaultAccepted range
Intake per dart (cm)The width one dart removes, both legs added together.50 and up
Dart leg to the apex (cm)From the dart point to where the intake is taken — the length of the dart leg.120 and up
Apex to hem (cm)Dart point to hem; the swing when you rotate the dart scales with it.300 and up

Step by step

FormulaRotation angle = 2 × asin(Intake per dart ÷ 2 ÷ Dart leg to the apex), Hem swing = Rotation angle × π ÷ 180 × Apex to hem
With the default numbersRotation angle = 2 × asin(5 ÷ 2 ÷ 12), Hem swing = Rotation angle × π ÷ 180 × 30
AnswerRotation angle = 24 °

Quick reference table

Results when only Intake per dart (cm) changes and everything else stays put.

Intake per dart (cm)Rotation angle (°)Hem swing (cm)
2.5126.3
3.75189.4
52412.6
7.536.419.1
1049.225.8

What each result means

ResultAt default values
Rotation angle (°)The angle the dart opens at its point; moving the dart never changes it.24
Hem swing (cm)How far the hem opens out when the dart is rotated away.12.6

Common mistakes

The same angle means different intakes at different lengths — 24.0° taken 6 cm from the apex is only 2.5 cm. So copying "a 5 cm dart" to another position doubles the angle and makes the bust point out like a cone. Stop the dart point 1.5–2 cm short of the bust point rather than on it, or you build that cone deliberately. Past about 30° a single dart cannot swallow the shaping: split it into two side by side, or convert to a princess seam. Actually rotating the paper is always more reliable than the arithmetic.

Glossary

Intake per dart
The width one dart removes, both legs added together.
Dart leg to the apex
From the dart point to where the intake is taken — the length of the dart leg.
Apex to hem
Dart point to hem; the swing when you rotate the dart scales with it.
Rotation angle
The angle the dart opens at its point; moving the dart never changes it.
Hem swing
How far the hem opens out when the dart is rotated away.

Frequently asked questions

Q. How is Bust Dart Rotation Calculator calculated?

Rotation angle = 2 × asin(Intake per dart ÷ 2 ÷ Dart leg to the apex), Hem swing = Rotation angle × π ÷ 180 × Apex to hem — A dart is a fold of paper about its point, so it can be handled as an angle. With a 5 cm intake as the chord and 12 cm to the apex as the radius, that is 2 × asin(2.5 ÷ 12) = 24.0°. The angle does not change wherever you move it: close the side dart and open a waist dart, or move it to the shoulder or the neckline, and the same 24.0° travels. With 30 cm from apex to hem, rotating the dart swings the hem open by 0.42 rad × 30 = 12.6 cm.

Q. Can you walk through an example?

With Intake per dart 5cm, Dart leg to the apex 12cm, Apex to hem 30cm, the answer is Rotation angle 24°.

Q. What do I need to enter?

Enter Intake per dart, Dart leg to the apex, Apex to hem. The result recalculates as you type, and an empty box counts as zero.

Q. How much does the answer move if I change a number?

Changing only Intake per dart (cm) moves the answer to Intake per dart (cm) 2.5 → Rotation angle (°) 12 and Intake per dart (cm) 10 → Rotation angle (°) 49.2. The table below lays out five steps.

Q. How are the numbers rounded?

Money is shown to the nearest whole unit, percentages to one decimal place and everything else to two. What you see is rounded; the calculation itself carries the unrounded value forward.

Q. Anything to watch out for?

The same angle means different intakes at different lengths — 24.0° taken 6 cm from the apex is only 2.5 cm. So copying "a 5 cm dart" to another position doubles the angle and makes the bust point out like a cone. Stop the dart point 1.5–2 cm short of the bust point rather than on it, or you build that cone deliberately. Past about 30° a single dart cannot swallow the shaping: split it into two side by side, or convert to a princess seam. Actually rotating the paper is always more reliable than the arithmetic.

Related calculators

Materials differ in density and absorption. If your label states a figure, use it — the defaults here are only common values.