The sagitta is the height of an
arc.

It is the perpendicular from the midpoint of the arc's chord to the arc itself.

It is the perpendicular from the midpoint of the arc's chord to the arc itself.

Try this Drag the orange dot to move the chord. Note how the sagitta is recalculated.

In the figure above, the blue arc is a portion of the circle that is cut off by the horizontal chord. The sagitta is the vertical line from the midpoint of the chord to the arc itself. It is a measure of the 'height' of the arc.

The length of the chord, sagitta and radius of the arc are inter-related, and if you know any two you can calculate the third.

You can find the length of the sagitta using the formula: where:

s |
is the length of the sagitta |

r |
is the radius of the arc |

l |
is one half of distance across the base of the arc (half the chord length) |

Notice that there are two results due to the "plus or minus" in the formula. The smaller one is the sagitta as show in the diagram above. The other is the longer sagitta that goes the other way across the larger part of the circle:

a |
is the length of the arc |

r |
is the radius of the arc |

l |
is one half of distance across the base of the arc (half the chord length) |

* Note the sine function should calculated in radians.

Then, knowing the radius and half the chord length, proceed as in method 1 above.
s |
is the length of the sagitta |

r |
is the radius of the arc |

l |
is one half of distance across the base of the arc (half the chord length) |

s |
is the length of the sagitta |

r |
is the radius of the arc |

l |
is one half of distance across the base of the arc (half the chord length) |

** Note** In all the above formulae, the length

ENTER RADIUS AND EITHER L or A | ||

Radius R | clear | |

Chord length L | clear | |

or | ||

Arc Length A | clear | |

- In the above applet click 'reset', and 'hide details'.
- Drag the orange dot to reposition the chord.
- Calculate the length of the sagitta.
- Click 'show details' to check your result.

- Circle definition
- Radius of a circle
- Diameter of a circle
- Circumference of a circle
- Parts of a circle (diagram)
- Semicircle definition
- Tangent
- Secant
- Chord
- Intersecting chords theorem
- Intersecting secant lengths theorem
- Intersecting secant angles theorem
- Area of a circle
- Concentric circles
- Annulus
- Area of an annulus
- Sector of a circle
- Area of a circle sector
- Segment of a circle
- Area of a circle segment (given central angle)
- Area of a circle segment (given segment height)

- Basic Equation of a Circle (Center at origin)
- General Equation of a Circle (Center anywhere)
- Parametric Equation of a Circle

- Arc
- Arc length
- Arc angle measure
- Adjacent arcs
- Major/minor arcs
- Intercepted Arc
- Sector of a circle
- Radius of an arc or segment, given height/width
- Sagitta - height of an arc or segment

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All rights reserved