Sag Calculator
Free online sag calculator — compute sagitta (arc height) from radius of curvature and chord diameter. Perfect for suspension tuning, arch design, and construction geometry.
About This Calculator
The Sag Calculator computes the sagitta (also called SAG or arc height) of a curved surface — the perpendicular distance from the midpoint of a chord to the highest point of the arc above it. This measurement is essential in mechanical engineering, vehicle suspension tuning, architectural arch design, and construction geometry.
The calculation uses the standard sagitta formula derived from circular geometry: sag = R - √(R² - (D/2)²), where R is the radius of curvature and D is the chord diameter (the straight-line width of the arc). The formula comes from applying the Pythagorean theorem to the right triangle formed by the radius, half-chord, and the radius minus sagitta.
The sagitta value determines how much a surface curves — a larger sagitta means a deeper, more pronounced arc. This is critical for setting suspension preload on motorcycles and mountain bikes (where rider sag is typically 25-35% of total suspension travel), for calculating the rise of architectural arches, and for determining the curvature of lenses and mirrors in optics.
Regional Notes
India: Sagitta calculations are used in civil engineering for arched bridge design, dome construction, and curved roof structures. Builders often work in meters or millimeters.
US: In the US, sagitta is commonly used for suspension tuning (motorcycle and automotive), firearm scope mounting, and architectural arch construction. Measurements are often in inches or feet.
UK: UK engineers use sagitta for structural arch design, historic building restoration, and vehicle suspension setup. Metric units (mm or m) are standard in engineering, while imperial may appear in automotive contexts.
Frequently Asked Questions
What is sagitta (SAG)?
Sagitta, also called SAG, is the depth or height of an arc — the distance from the midpoint of a chord to the highest point of the arc above it. In engineering and construction, sagitta describes how much a curved surface deviates from a straight line connecting its endpoints.
How do I calculate sagitta?
Use the formula: sag = R - sqrt(R² - (D/2)²), where R is the radius of curvature and D is the chord diameter. First find the radius of curvature, then measure the chord diameter across the arc, and apply the formula to get the sagitta height.
What is the sagitta formula?
The sagitta formula is sag = R - sqrt(R² - (d/2)²), where R is the radius of curvature and d is the chord length (diameter). This formula derives from the Pythagorean theorem applied to a circle segment and works for any circular arc where d is less than 2R.
Why is sag adjustment important in suspension?
Proper sag adjustment ensures the suspension operates in its optimal range, maintaining consistent wheel contact with the road. This improves traction, ride comfort, handling stability, and prevents bottoming out or excessive rebound in vehicles like motorcycles and mountain bikes.
Can sagitta be larger than the radius?
No, sagitta cannot exceed the radius. The maximum possible sagitta equals the radius itself, which occurs when the chord diameter equals twice the radius — at that point the chord is a full diameter of the circle and the sagitta equals the radius. For any valid circular segment, sagitta is always less than the radius.
What units should I use for the sag calculator?
You can use any consistent unit (meters, feet, inches, etc.) for both radius and diameter — the sagitta will be in the same unit. The calculator defaults to meters but works correctly as long as both inputs use the same unit of measurement.
How do I use this sag calculator?
Enter the radius of curvature and the chord diameter (or width) of the curved surface. Click Calculate Sag to instantly compute the sagitta value. You can toggle between the Sag vs Diameter chart and the Arc Geometry comparison to visualize how the arc dimensions relate.
Is sagitta used in architecture?
Yes, sagitta is widely used in architecture and construction for designing arches, vaulted ceilings, curved facades, and arched windows. Knowing the sagitta helps builders determine the rise of an arch given its span and radius, ensuring structural integrity and aesthetic proportions.