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Tap Drill worksheet

Grades 6–7 · CCSS 6.EE.A.2.c, 7.RP.A.3

Solve each problem and show your work. Round answers to 2 decimal places where needed.

  1. Problem 1.
    • Thread system: ISO metric
    • Thread size: M1.6 × 0.35
    • Percentage of thread: 65%

    Find: Nearest standard drill diameter

  2. Problem 2.
    • Thread system: ISO metric
    • Thread size: Other (enter diameter and pitch)
    • Major diameter: 8 mm
    • Pitch: 1.75 mm
    • Percentage of thread: 70%

    Find: Nearest standard drill diameter

  3. Problem 3.
    • Thread system: Unified inch (UNC/UNF)
    • Thread size: Other (enter diameter and pitch)
    • Major diameter: 0.5 in
    • Threads per inch: 12
    • Percentage of thread: 50%

    Find: Nearest standard drill diameter

  4. Problem 4.
    • Thread system: Unified inch (UNC/UNF)
    • Thread size: #5-40 UNC
    • Percentage of thread: 50%

    Find: Nearest standard drill diameter

  5. Problem 5.
    • Thread system: Unified inch (UNC/UNF)
    • Thread size: #1-72 UNF
    • Percentage of thread: 60%

    Find: Nearest standard drill diameter

  6. Problem 6.
    • Thread system: ISO metric
    • Thread size: M6 × 1
    • Percentage of thread: 55%

    Find: Nearest standard drill diameter

  7. Problem 7.
    • Thread system: Unified inch (UNC/UNF)
    • Thread size: #12-24 UNC
    • Percentage of thread: 65%

    Find: Nearest standard drill diameter

  8. Problem 8.
    • Thread system: ISO metric
    • Thread size: M12 × 1.5 (fine)
    • Percentage of thread: 70%

    Find: Nearest standard drill diameter

  9. Problem 9.
    • Thread system: Unified inch (UNC/UNF)
    • Thread size: 1/2-20 UNF
    • Percentage of thread: 60%

    Find: Nearest standard drill diameter

  10. Problem 10.
    • Thread system: ISO metric
    • Thread size: Other (enter diameter and pitch)
    • Major diameter: 8 mm
    • Pitch: 1.75 mm
    • Percentage of thread: 50%

    Find: Nearest standard drill diameter

Answer key: Tap Drill worksheet

  1. 1. Nearest standard drill diameter: 1.3 mm

    1. M1.6 × 0.35: the outside diameter (D) and the distance between threads (P)

      D, P=1.6 mm, 0.35 mm
    2. Work out how much the threads cut into the diameter for 65% thread: 0.01299 × % × pitch

      0.01299×65×0.35=0.2955225 mm
    3. Take that off the outside diameter to get the exact drill size

      1.6−0.2955225=1.3044775 mm
    4. Pick the nearest drill you can actually buy: 1.3 mm

      1.3 mm=1.3 mm
    5. Run the formula backward to see how much thread that drill really leaves

      1.6−1.30.01299×0.35=65.98%
  2. 2. Nearest standard drill diameter: 6.4 mm

    1. M8 × 1.75: the outside diameter (D) and the distance between threads (P)

      D, P=8 mm, 1.75 mm
    2. Work out how much the threads cut into the diameter for 70% thread: 0.01299 × % × pitch

      0.01299×70×1.75=1.591275 mm
    3. Take that off the outside diameter to get the exact drill size

      8−1.591275=6.408725 mm
    4. Pick the nearest drill you can actually buy: 6.4 mm

      6.4 mm=6.4 mm
    5. Run the formula backward to see how much thread that drill really leaves

      8−6.40.01299×1.75=70.38%
  3. 3. Nearest standard drill diameter: 0.4531 in

    1. 0.5-12: the pitch is one inch divided by the threads per inch

      112=0.08333333 in
    2. Work out how much the threads cut into the diameter for 50% thread: 0.01299 × % × pitch

      0.01299×50×0.08333333=0.054125 in
    3. Take that off the outside diameter to get the exact drill size

      0.5−0.054125=0.445875 in
    4. Pick the nearest drill you can actually buy: 29/64"

      29/64"=0.4531 in
    5. Run the formula backward to see how much thread that drill really leaves

      0.5−0.45310.01299×0.08333333=43.3%
  4. 4. Nearest standard drill diameter: 0.1094 in

    1. #5-40 UNC: the pitch is one inch divided by the threads per inch

      140=0.025 in
    2. Work out how much the threads cut into the diameter for 50% thread: 0.01299 × % × pitch

      0.01299×50×0.025=0.0162375 in
    3. Take that off the outside diameter to get the exact drill size

      0.125−0.0162375=0.1087625 in
    4. Pick the nearest drill you can actually buy: 7/64"

      7/64"=0.1094 in
    5. Run the formula backward to see how much thread that drill really leaves

      0.125−0.10940.01299×0.025=48.11%
  5. 5. Nearest standard drill diameter: 0.0625 in

    1. #1-72 UNF: the pitch is one inch divided by the threads per inch

      172=0.01388889 in
    2. Work out how much the threads cut into the diameter for 60% thread: 0.01299 × % × pitch

      0.01299×60×0.01388889=0.010825 in
    3. Take that off the outside diameter to get the exact drill size

      0.073−0.010825=0.062175 in
    4. Pick the nearest drill you can actually buy: 1/16"

      1/16"=0.0625 in
    5. Run the formula backward to see how much thread that drill really leaves

      0.073−0.06250.01299×0.01388889=58.2%
  6. 6. Nearest standard drill diameter: 5.3 mm

    1. M6 × 1: the outside diameter (D) and the distance between threads (P)

      D, P=6 mm, 1 mm
    2. Work out how much the threads cut into the diameter for 55% thread: 0.01299 × % × pitch

      0.01299×55×1=0.71445 mm
    3. Take that off the outside diameter to get the exact drill size

      6−0.71445=5.28555 mm
    4. Pick the nearest drill you can actually buy: 5.3 mm

      5.3 mm=5.3 mm
    5. Run the formula backward to see how much thread that drill really leaves

      6−5.30.01299×1=53.89%
  7. 7. Nearest standard drill diameter: 0.18 in

    1. #12-24 UNC: the pitch is one inch divided by the threads per inch

      124=0.04166667 in
    2. Work out how much the threads cut into the diameter for 65% thread: 0.01299 × % × pitch

      0.01299×65×0.04166667=0.03518125 in
    3. Take that off the outside diameter to get the exact drill size

      0.216−0.03518125=0.18081875 in
    4. Pick the nearest drill you can actually buy: #15

      #15=0.18 in
    5. Run the formula backward to see how much thread that drill really leaves

      0.216−0.180.01299×0.04166667=66.51%
  8. 8. Nearest standard drill diameter: 10.6 mm

    1. M12 × 1.5 (fine): the outside diameter (D) and the distance between threads (P)

      D, P=12 mm, 1.5 mm
    2. Work out how much the threads cut into the diameter for 70% thread: 0.01299 × % × pitch

      0.01299×70×1.5=1.36395 mm
    3. Take that off the outside diameter to get the exact drill size

      12−1.36395=10.63605 mm
    4. Pick the nearest drill you can actually buy: 10.6 mm

      10.6 mm=10.6 mm
    5. Run the formula backward to see how much thread that drill really leaves

      12−10.60.01299×1.5=71.85%
  9. 9. Nearest standard drill diameter: 0.4688 in

    1. 1/2-20 UNF: the pitch is one inch divided by the threads per inch

      120=0.05 in
    2. Work out how much the threads cut into the diameter for 60% thread: 0.01299 × % × pitch

      0.01299×60×0.05=0.03897 in
    3. Take that off the outside diameter to get the exact drill size

      0.5−0.03897=0.46103 in
    4. Pick the nearest drill you can actually buy: 15/32"

      15/32"=0.4688 in
    5. Run the formula backward to see how much thread that drill really leaves

      0.5−0.46880.01299×0.05=48.11%
  10. 10. Nearest standard drill diameter: 6.9 mm

    1. M8 × 1.75: the outside diameter (D) and the distance between threads (P)

      D, P=8 mm, 1.75 mm
    2. Work out how much the threads cut into the diameter for 50% thread: 0.01299 × % × pitch

      0.01299×50×1.75=1.136625 mm
    3. Take that off the outside diameter to get the exact drill size

      8−1.136625=6.863375 mm
    4. Pick the nearest drill you can actually buy: 6.9 mm

      6.9 mm=6.9 mm
    5. Run the formula backward to see how much thread that drill really leaves

      8−6.90.01299×1.75=48.39%