Bolt Circle worksheet

1. Center-to-center spacing of neighboring holes: 1.16 mm

1. Radius: half the bolt circle diameter

   $\frac{4.5\text{\hspace{0.17em}mm}}{2}$$=2.25\text{\hspace{0.17em}mm}$

2. Angle between neighboring holes: a full turn divided by the number of holes

   $\frac{360\text{\hspace{0.17em}°}}{12}$$=30\text{\hspace{0.17em}°}$

3. Find hole 1's X position: start at the center, then add the radius times the cosine of its angle, the sideways part

   $0+2.25\times \text{cos}90\text{\hspace{0.17em}°}$$=0\text{\hspace{0.17em}mm}$

4. Find hole 1's Y position: start at the center, then add the radius times the sine of its angle, the up-and-down part

   $0+2.25\times \text{sin}90\text{\hspace{0.17em}°}$$=2.25\text{\hspace{0.17em}mm}$

5. Each next hole adds 30° counterclockwise, so hole 2 sits at 120°

   $\mathrm{(x₂,\; y₂)}$$=\text{(}\mathrm{-1.125}\text{,}1.948557\text{)}$

6. Find the straight-line spacing between neighboring hole centers (the chord), the diameter times sin(180° ÷ n), so you can check it with calipers

   $4.5\times \text{sin}15\text{\hspace{0.17em}°}$$=1.164686\text{\hspace{0.17em}mm}$

2. Center-to-center spacing of neighboring holes: 3.53 in

1. Radius: half the bolt circle diameter

   $\frac{6\text{\hspace{0.17em}in}}{2}$$=3\text{\hspace{0.17em}in}$

2. Angle between neighboring holes: a full turn divided by the number of holes

   $\frac{360\text{\hspace{0.17em}°}}{5}$$=72\text{\hspace{0.17em}°}$

3. Find hole 1's X position: start at the center, then add the radius times the cosine of its angle, the sideways part

   $0+3\times \text{cos}90\text{\hspace{0.17em}°}$$=0\text{\hspace{0.17em}in}$

4. Find hole 1's Y position: start at the center, then add the radius times the sine of its angle, the up-and-down part

   $0+3\times \text{sin}90\text{\hspace{0.17em}°}$$=3\text{\hspace{0.17em}in}$

5. Each next hole adds 72° clockwise, so hole 2 sits at 18°

   $\mathrm{(x₂,\; y₂)}$$=\text{(}2.85317\text{,}0.927051\text{)}$

6. Find the straight-line spacing between neighboring hole centers (the chord), the diameter times sin(180° ÷ n), so you can check it with calipers

   $6\times \text{sin}36\text{\hspace{0.17em}°}$$=3.526712\text{\hspace{0.17em}in}$

3. Center-to-center spacing of neighboring holes: 1.18 in

1. Radius: half the bolt circle diameter

   $\frac{2\text{\hspace{0.17em}in}}{2}$$=1\text{\hspace{0.17em}in}$

2. Angle between neighboring holes: a full turn divided by the number of holes

   $\frac{360\text{\hspace{0.17em}°}}{5}$$=72\text{\hspace{0.17em}°}$

3. Find hole 1's X position: start at the center, then add the radius times the cosine of its angle, the sideways part

   $0+1\times \text{cos}15\text{\hspace{0.17em}°}$$=0.965926\text{\hspace{0.17em}in}$

4. Find hole 1's Y position: start at the center, then add the radius times the sine of its angle, the up-and-down part

   $0+1\times \text{sin}15\text{\hspace{0.17em}°}$$=0.258819\text{\hspace{0.17em}in}$

5. Each next hole adds 72° counterclockwise, so hole 2 sits at 87°

   $\mathrm{(x₂,\; y₂)}$$=\text{(}0.052336\text{,}0.99863\text{)}$

6. Find the straight-line spacing between neighboring hole centers (the chord), the diameter times sin(180° ÷ n), so you can check it with calipers

   $2\times \text{sin}36\text{\hspace{0.17em}°}$$=1.175571\text{\hspace{0.17em}in}$

4. Center-to-center spacing of neighboring holes: 1.18 in

1. Radius: half the bolt circle diameter

   $\frac{2\text{\hspace{0.17em}in}}{2}$$=1\text{\hspace{0.17em}in}$

2. Angle between neighboring holes: a full turn divided by the number of holes

   $\frac{360\text{\hspace{0.17em}°}}{5}$$=72\text{\hspace{0.17em}°}$

3. Find hole 1's X position: start at the center, then add the radius times the cosine of its angle, the sideways part

   $0+1\times \text{cos}45\text{\hspace{0.17em}°}$$=0.707107\text{\hspace{0.17em}in}$

4. Find hole 1's Y position: start at the center, then add the radius times the sine of its angle, the up-and-down part

   $0+1\times \text{sin}45\text{\hspace{0.17em}°}$$=0.707107\text{\hspace{0.17em}in}$

5. Each next hole adds 72° counterclockwise, so hole 2 sits at 117°

   $\mathrm{(x₂,\; y₂)}$$=\text{(}\mathrm{-0.45399}\text{,}0.891007\text{)}$

6. Find the straight-line spacing between neighboring hole centers (the chord), the diameter times sin(180° ÷ n), so you can check it with calipers

   $2\times \text{sin}36\text{\hspace{0.17em}°}$$=1.175571\text{\hspace{0.17em}in}$

5. Center-to-center spacing of neighboring holes: 1.18 in

1. Radius: half the bolt circle diameter

   $\frac{2\text{\hspace{0.17em}in}}{2}$$=1\text{\hspace{0.17em}in}$

2. Angle between neighboring holes: a full turn divided by the number of holes

   $\frac{360\text{\hspace{0.17em}°}}{5}$$=72\text{\hspace{0.17em}°}$

3. Find hole 1's X position: start at the center, then add the radius times the cosine of its angle, the sideways part

   $0+1\times \text{cos}30\text{\hspace{0.17em}°}$$=0.866025\text{\hspace{0.17em}in}$

4. Find hole 1's Y position: start at the center, then add the radius times the sine of its angle, the up-and-down part

   $0+1\times \text{sin}30\text{\hspace{0.17em}°}$$=0.5\text{\hspace{0.17em}in}$

5. Each next hole adds 72° counterclockwise, so hole 2 sits at 102°

   $\mathrm{(x₂,\; y₂)}$$=\text{(}\mathrm{-0.207912}\text{,}0.978148\text{)}$

6. Find the straight-line spacing between neighboring hole centers (the chord), the diameter times sin(180° ÷ n), so you can check it with calipers

   $2\times \text{sin}36\text{\hspace{0.17em}°}$$=1.175571\text{\hspace{0.17em}in}$

6. Center-to-center spacing of neighboring holes: 1.15 mm

1. Radius: half the bolt circle diameter

   $\frac{3\text{\hspace{0.17em}mm}}{2}$$=1.5\text{\hspace{0.17em}mm}$

2. Angle between neighboring holes: a full turn divided by the number of holes

   $\frac{360\text{\hspace{0.17em}°}}{8}$$=45\text{\hspace{0.17em}°}$

3. Find hole 1's X position: start at the center, then add the radius times the cosine of its angle, the sideways part

   $0+1.5\times \text{cos}30\text{\hspace{0.17em}°}$$=1.299038\text{\hspace{0.17em}mm}$

4. Find hole 1's Y position: start at the center, then add the radius times the sine of its angle, the up-and-down part

   $0+1.5\times \text{sin}30\text{\hspace{0.17em}°}$$=0.75\text{\hspace{0.17em}mm}$

5. Each next hole adds 45° counterclockwise, so hole 2 sits at 75°

   $\mathrm{(x₂,\; y₂)}$$=\text{(}0.388229\text{,}1.448889\text{)}$

6. Find the straight-line spacing between neighboring hole centers (the chord), the diameter times sin(180° ÷ n), so you can check it with calipers

   $3\times \text{sin}22.5\text{\hspace{0.17em}°}$$=1.14805\text{\hspace{0.17em}mm}$

7. Center-to-center spacing of neighboring holes: 3 mm

1. Radius: half the bolt circle diameter

   $\frac{6\text{\hspace{0.17em}mm}}{2}$$=3\text{\hspace{0.17em}mm}$

2. Angle between neighboring holes: a full turn divided by the number of holes

   $\frac{360\text{\hspace{0.17em}°}}{6}$$=60\text{\hspace{0.17em}°}$

3. Find hole 1's X position: start at the center, then add the radius times the cosine of its angle, the sideways part

   $0+3\times \text{cos}45\text{\hspace{0.17em}°}$$=2.12132\text{\hspace{0.17em}mm}$

4. Find hole 1's Y position: start at the center, then add the radius times the sine of its angle, the up-and-down part

   $0+3\times \text{sin}45\text{\hspace{0.17em}°}$$=2.12132\text{\hspace{0.17em}mm}$

5. Each next hole adds 60° counterclockwise, so hole 2 sits at 105°

   $\mathrm{(x₂,\; y₂)}$$=\text{(}\mathrm{-0.776457}\text{,}2.897777\text{)}$

6. Find the straight-line spacing between neighboring hole centers (the chord), the diameter times sin(180° ÷ n), so you can check it with calipers

   $6\times \text{sin}30\text{\hspace{0.17em}°}$$=3\text{\hspace{0.17em}mm}$

8. Center-to-center spacing of neighboring holes: 4.24 mm

1. Radius: half the bolt circle diameter

   $\frac{6\text{\hspace{0.17em}mm}}{2}$$=3\text{\hspace{0.17em}mm}$

2. Angle between neighboring holes: a full turn divided by the number of holes

   $\frac{360\text{\hspace{0.17em}°}}{4}$$=90\text{\hspace{0.17em}°}$

3. Find hole 1's X position: start at the center, then add the radius times the cosine of its angle, the sideways part

   $0+3\times \text{cos}15\text{\hspace{0.17em}°}$$=2.897777\text{\hspace{0.17em}mm}$

4. Find hole 1's Y position: start at the center, then add the radius times the sine of its angle, the up-and-down part

   $0+3\times \text{sin}15\text{\hspace{0.17em}°}$$=0.776457\text{\hspace{0.17em}mm}$

5. Each next hole adds 90° counterclockwise, so hole 2 sits at 105°

   $\mathrm{(x₂,\; y₂)}$$=\text{(}\mathrm{-0.776457}\text{,}2.897777\text{)}$

6. Find the straight-line spacing between neighboring hole centers (the chord), the diameter times sin(180° ÷ n), so you can check it with calipers

   $6\times \text{sin}45\text{\hspace{0.17em}°}$$=4.242641\text{\hspace{0.17em}mm}$

9. Center-to-center spacing of neighboring holes: 0.93 in

1. Radius: half the bolt circle diameter

   $\frac{3\text{\hspace{0.17em}in}}{2}$$=1.5\text{\hspace{0.17em}in}$

2. Angle between neighboring holes: a full turn divided by the number of holes

   $\frac{360\text{\hspace{0.17em}°}}{10}$$=36\text{\hspace{0.17em}°}$

3. Find hole 1's X position: start at the center, then add the radius times the cosine of its angle, the sideways part

   $0+1.5\times \text{cos}30\text{\hspace{0.17em}°}$$=1.299038\text{\hspace{0.17em}in}$

4. Find hole 1's Y position: start at the center, then add the radius times the sine of its angle, the up-and-down part

   $0+1.5\times \text{sin}30\text{\hspace{0.17em}°}$$=0.75\text{\hspace{0.17em}in}$

5. Each next hole adds 36° counterclockwise, so hole 2 sits at 66°

   $\mathrm{(x₂,\; y₂)}$$=\text{(}0.610105\text{,}1.370318\text{)}$

6. Find the straight-line spacing between neighboring hole centers (the chord), the diameter times sin(180° ÷ n), so you can check it with calipers

   $3\times \text{sin}18\text{\hspace{0.17em}°}$$=0.927051\text{\hspace{0.17em}in}$

10. Center-to-center spacing of neighboring holes: 0.77 in

1. Radius: half the bolt circle diameter

   $\frac{2\text{\hspace{0.17em}in}}{2}$$=1\text{\hspace{0.17em}in}$

2. Angle between neighboring holes: a full turn divided by the number of holes

   $\frac{360\text{\hspace{0.17em}°}}{8}$$=45\text{\hspace{0.17em}°}$

3. Find hole 1's X position: start at the center, then add the radius times the cosine of its angle, the sideways part

   $0+1\times \text{cos}90\text{\hspace{0.17em}°}$$=0\text{\hspace{0.17em}in}$

4. Find hole 1's Y position: start at the center, then add the radius times the sine of its angle, the up-and-down part

   $0+1\times \text{sin}90\text{\hspace{0.17em}°}$$=1\text{\hspace{0.17em}in}$

5. Each next hole adds 45° counterclockwise, so hole 2 sits at 135°

   $\mathrm{(x₂,\; y₂)}$$=\text{(}\mathrm{-0.707107}\text{,}0.707107\text{)}$

6. Find the straight-line spacing between neighboring hole centers (the chord), the diameter times sin(180° ÷ n), so you can check it with calipers

   $2\times \text{sin}22.5\text{\hspace{0.17em}°}$$=0.765367\text{\hspace{0.17em}in}$