The simplest way to measure a fillet radius is with a radius gauge, a set of curved metal leaves that you press against the fillet until one matches the curve exactly. For fillets where a gauge set doesn’t give you a clean match, you can calculate the radius mathematically using two easy measurements and a basic formula. Here’s how each method works and when to use it.
Using a Radius Gauge Set
A radius gauge (sometimes called a fillet gauge) is a fan of thin steel or plastic leaves, each machined to a specific radius on one or both edges. One side of each leaf is concave, the other convex. Concave edges measure outside (convex) curves, and convex edges measure inside (concave) curves like the corner of a fillet. Sets typically cover common increments: 1mm, 1.5mm, 2mm, 3mm, 5mm, 8mm, 10mm, and so on, matching standard cutting tool sizes used in machining.
To use one, select a leaf that looks close to the curve you’re measuring and press it into the fillet. Hold it up to a light source. If you see a gap between the leaf and the surface, the leaf’s radius doesn’t match. Try the next size up or down. When the leaf sits flush against the curve with no visible light gap, you’ve found the radius. The reading stamped on that leaf is your measurement.
Radius gauge sets are cheap, fast, and don’t need calibration. Their main limitation is resolution. If your fillet falls between two leaves in the set, you’ll only know the radius is somewhere in that range. For most shop work and weld inspections, that’s accurate enough.
Three-Point Adjustable Radius Gauges
For fillets that don’t match a fixed leaf, an adjustable radius gauge gives you a continuous reading instead of discrete steps. These tools have three contact points: one center point and two outer points that slide along a calibrated scale.
To use one, loosen the locking knob (often called the “brake”), then place the center contact point on the curve. Gently slide the pointer from the low end of the scale until both outer contact points also touch the surface. All three points must make contact with the curve simultaneously for an accurate reading. Once they do, tighten the brake and read the radius value directly from the scale. This method works on both concave and convex surfaces and handles odd sizes that fall between standard gauge leaves.
Calculating Radius With the Sagitta Method
When you can’t press a gauge into the fillet, or the radius is too large for your gauge set, you can calculate it from two simple measurements: the chord length and the sagitta (the height of the arc).
What You’re Measuring
Imagine drawing a straight line across the opening of the curved section. That straight line is the chord. Now measure the distance from the midpoint of that chord straight down (or up) to the deepest point of the curve. That perpendicular distance is the sagitta, often written as “s” or “h.”
The Formula
Once you have both measurements, the radius is:
R = (L² / 8h) + (h / 2)
Where L is the chord length and h is the sagitta. For example, if you measure a chord of 20mm across a fillet and the height from the chord’s midpoint to the curve is 2mm, the radius works out to (400 / 16) + (2 / 2) = 25 + 1 = 26mm.
This method is especially useful for large-radius fillets on castings, forgings, or structural welds where no gauge set goes high enough. All you need is a straightedge, a depth gauge or caliper, and a calculator. The accuracy depends entirely on how precisely you measure the chord and sagitta, so take your time positioning the straightedge and ensure it contacts both edges of the arc cleanly.
Optical and Digital Methods
For higher precision or production inspection, optical and digital tools remove the guesswork. A profile projector (optical comparator) magnifies the part’s silhouette onto a screen, where you overlay a radius template or use built-in software to fit a circle to the projected curve. Measuring microscopes work similarly, letting you evaluate radii, distances, and angles quickly under magnification.
Digital contour measuring systems take this further. A stylus traces the surface profile, and software automatically fits arcs to the recorded data, reporting the radius to micrometer-level accuracy. These systems are standard in manufacturing environments where tolerances are tight and dozens or hundreds of parts need checking. They’re overkill for a one-off measurement in a home shop, but if you have access to one, they give the most precise and repeatable results.
Choosing the Right Method
- Fixed radius gauge set: Best for quick checks on standard-size fillets. Works well for weld inspections, machined parts, and 3D-printed components where you just need to confirm the radius matches a specification.
- Adjustable three-point gauge: Best when the fillet radius is non-standard or you need a continuous measurement rather than a closest-match estimate.
- Sagitta calculation: Best for large radii, partial arcs, or situations where you can’t physically press a gauge into the fillet (recessed features, for instance).
- Optical or digital measurement: Best for tight tolerances, batch inspection, or documentation that requires traceable measurement data.
Tips for Accurate Results
Clean the surface before measuring. Paint, burrs, weld spatter, or debris will all throw off your reading, especially with contact methods like gauges. Even a thin layer of mill scale on a forging can introduce enough error to push you into the wrong size range.
Measure in more than one spot. Fillets aren’t always uniform, particularly on castings or hand-finished welds. Checking at two or three points along the fillet’s length tells you whether the radius is consistent or varies. If it varies, note the range rather than a single number.
When using the sagitta method, a longer chord gives a more forgiving measurement. Small errors in sagitta have less effect on the calculated radius when the chord is wide relative to the arc height. If you can, span as much of the curve as your straightedge allows.