Inspection and GD&T
Measuring dovetails with pins
Enter the dovetail angle, pin diameter and width to get the measurement over pins (male) or between pins (female).
Technical review pending. Formulas and values are cited. This notice comes down after a machinist review.
Measurement over pins (M)
in
M = a + D x (1 + cot(alpha / 2)) = 1.5000 + 0.25 x (1 + cot(60° / 2)) = 2.1830 in
2.1830 in (55.449 mm) over two 0.2500 in pins.
Pin constant (c)
in
c = D x (1 + cot(alpha / 2)) = 0.25 x (1 + cot(60° / 2)) = 0.6830 in
Pin touches the flank 0.1875 in above the base and 0.2165 in from the corner. Enter the height H to check the pin size.
Source: Machinery's Handbook (measuring dovetail slides); the relation is derived from the pin geometry below
Metric results are shown to 0.001 mm because pin measurements are read that fine.
How it works
c = D x (1 + cot(alpha / 2)); male: M = a + c; female: M = a - c
| Symbol | Meaning | Unit |
|---|---|---|
| M | Measurement over pins (male) or between pins (female) | in or mm |
| a | Width between the sharp corners where the flanks meet the base the pins rest on: the narrow bottom of a male dovetail, the wide bottom of a female slot | in or mm |
| c | Pin constant: what two pins add to (male) or take from (female) the corner width | in or mm |
| D | Pin (gage pin or roll) diameter, both pins the same size | in or mm |
| alpha (α) | Flank angle, measured between the flank and the base | ° |
| W | Width at the top edge of the flanks, H above the base | in or mm |
| H | Dovetail height, base to the top edge of the flank | in or mm |
Where the formula comes from
- A pin touching both the base and the flank has its center on the line that splits the corner angle in half, D/2 above the base.
- The horizontal distance from the sharp corner to the pin center is (D/2) x cot(α/2).
- The pin's far side is another D/2 beyond that: (D/2) x (1 + cot(α/2)) from the corner.
- Two corners, two pins: c = D x (1 + cot(α/2)). Over pins on a male dovetail, M = a + c. Between pins in a female slot, M = a - c.
Width at a different height
Each flank leans cot(α) per unit of height, so the width changes by 2 x h x cot(α) over a height h. A male dovetail gets wider going up from the base; a female slot gets narrower going up. When the drawing gives the top width W and height H: a = W - 2 x H x cot(α) for a male dovetail, a = W + 2 x H x cot(α) for a female slot.
Worked example: male dovetail over pins
60° male dovetail, a = 1.500 in at the base corners, two 0.250 in pins.
- Half the angle: 60° / 2 = 30°; cot(30°) = 1.7321.
- Pin constant: c = 0.250 x (1 + 1.7321) = 0.250 x 2.7321 = 0.6830 in.
- Over pins: M = a + c = 1.5000 + 0.6830 = 2.1830 in.
- Pin check: contact is (0.250 / 2) x (1 + cos(60°)) = 0.125 x 1.5 = 0.1875 in above the base, which must be below the top of the flank.
Result: 2.1830 in over pins (55.449 mm).
Worked example: female slot from the top width
60° female dovetail slot, top opening W = 1.000 in, depth H = 0.375 in, two 0.250 in pins.
- Width change: 2 x 0.375 x cot(60°) = 2 x 0.375 x 0.5774 = 0.4330 in.
- Bottom corner width: a = W + 0.4330 = 1.0000 + 0.4330 = 1.4330 in.
- Pin constant, same as above: c = 0.6830 in.
- Between pins: M = a - c = 1.4330 - 0.6830 = 0.7500 in.
- Pin check: largest pin = 2 x 0.375 / (1 + cos(60°)) = 0.750 / 1.5 = 0.5000 in. The 0.250 in pin is well under it.
Result: 0.7500 in between pins (19.050 mm).
Pin size
The pin has to touch the flank, not the top corner of the dovetail. It touches the flank (D/2) x (1 + cos(α)) above the base, so the pin diameter must stay under 2 x H / (1 + cos(α)). At 60° that is 1.333 x H. The pin also touches the base and the flank (D/2) x cot(α/2) from the sharp corner, 0.866 x D at 60°; both contacts have to land on flat surface, past any relief groove or radius in the corner.
Shop notes
- Both pins must be the same diameter. Mike each pin before you use the number.
- The formula uses the sharp corner where the flank and base lines meet. A relief groove or corner radius does not change a, as long as the pins sit on flat surface past it.
- Deburr the flanks and base first. A burr under a pin reads as oversize.
- For a female slot, measure between the pins with an inside micrometer, gage blocks or pin gages.
FAQ
What is the pin constant c for a 60° dovetail with 0.250 in pins?
c = D x (1 + cot(30°)) = 0.250 x (1 + 1.7321) = 0.6830 in. Add it to a for a male dovetail (over pins), subtract it for a female dovetail (between pins).
What is c for a 55° dovetail?
c = D x (1 + cot(27.5°)) = D x 2.9210. With 0.250 in pins, c = 0.7302 in.
How do you measure a female dovetail with pins?
Set a pin in each bottom corner and measure between them: M = a - c. A 60° slot with a 1.000 in top opening, 0.375 in deep, has a = 1.4330 in; with 0.250 in pins, M = 1.4330 - 0.6830 = 0.7500 in.
What size pin should you use to measure a dovetail?
One that touches the flank below its top edge. The contact sits (D/2) x (1 + cos(α)) above the base, so the pin must be smaller than 2 x H / (1 + cos(α)). For a 60° dovetail 0.375 in high that limit is 0.5000 in, so a 0.250 in pin works.
How much does dovetail width change with height?
2 x h x cot(α) for a height h. On a 60° dovetail, 0.375 in of height changes the width by 2 x 0.375 x 0.5774 = 0.4330 in.
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