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newSchoolWorks.com › VoTechWorks › Business & Cross-Cutting › Locksmith & Security Systems › Lock Codes, Key Origination & Decoding › Lesson 1
BUS-LOCK72-08 · Lesson 1 · 12 clock hours · theory

Code Systems, Bitting Mathematics & MACS Rules

Objective. Given a manufacturer's depth-and-space specification sheet, the student will calculate valid bitting combinations and identify cuts that violate Maximum Adjacent Cut Specification (MACS) with 100% accuracy on a written problem set.

⚠ Pending professional review

This lesson, its worked examples and its practice questions has not yet been verified by a credentialed professional in the field or by a certification or approval body. It is a study draft and may contain errors. Do not use it as instructions for work on a job site or on live equipment. Always follow your instructor, your supervising professional, and current official references and regulations.

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What a Bitting Code Tells You

Every key cut on a pin-tumbler key has a number assigned to it called a bitting. That number corresponds to a precise depth below the key's shoulder or tip. Manufacturers publish depth-and-space specification sheets that define two things: (1) the exact vertical distance (depth) each cut number represents, and (2) the horizontal distance between cut positions (spacing). Without this data, a key blank is just a piece of metal; with it, a locksmith can originate or duplicate a key entirely from code—no original key required.

Manufacturers divide the total range of cut depth into discrete steps. Kwikset, for example, uses a system where each bitting number from 1 (shallowest) through 6 (deepest) is separated by a fixed increment. Schlage C keyway uses numbers 0 through 9, giving ten depth levels. The total number of theoretical bitting combinations for any key system is:

Total combinations = D^P

where D is the number of depth levels and P is the number of active cut positions on the key.

Depth and Spacing

Each cut position is measured from a reference point—usually the key tip or shoulder—at a fixed spacing interval. Manufacturers specify this in thousandths of an inch (or millimeters in metric systems). When you originate a key from code, you set your code machine or depth gauge to the published depth for each bitting number and cut each position at the correct spacing. Any error in depth or spacing can cause the key to fail to operate or to damage the cylinder.

The key section (also called the key profile or keyway) determines which blank fits which cylinder. Two keys may have identical bittings but different sections and will not interchange. Always confirm the correct blank number from a current code reference before cutting.

The Shear Line and Why It Matters

Inside a pin-tumbler cylinder, spring-loaded driver pins sit above key pins (bottom pins). When no key is inserted, the gap between driver pin and key pin sits below the shear line, blocking rotation. When the correct key is inserted, each cut lifts the stack so that every driver-pin/key-pin boundary aligns exactly at the shear line—the interface between the rotating plug and the stationary shell. The cylinder can then turn. A cut that is too deep lifts the stack too high; too shallow leaves it too low. Either way, the plug cannot rotate.

This is why bitting mathematics must be exact. Even one cut that is off by a single depth increment will prevent operation.

Maximum Adjacent Cut Specification (MACS)

Manufacturers impose a rule called the Maximum Adjacent Cut Specification (MACS). MACS defines the largest allowable difference in bitting depth between any two neighboring cut positions on the same key. The reason is mechanical: if adjacent cuts differ by too many depth levels, the key blade cannot physically guide the driver pins to the shear line—the sharp angle between cuts causes the key to bind or the pins to hang up on the edge of the cut rather than lift cleanly.

To check a bitting for MACS compliance:

1. Write the bitting sequence in order (position 1 through the last position).

2. Subtract each cut number from the number immediately next to it; take the absolute value (ignore negatives).

3. If any adjacent difference exceeds the manufacturer's stated MACS value, that bitting is invalid.

For example, if the MACS is 4 and positions 3 and 4 read `2` and `7`, the difference is 5—a MACS violation. That combination would not appear in a legitimate code book entry and should never be cut.

MACS values differ by manufacturer. Always consult the published specification sheet for the system you are working on rather than assuming a universal value.

Using a Key Code Reference

Published code books such as the Ilco Key Blank Reference or the Kaba Ilco Key Code Manual list key codes organized by manufacturer, keyway, and blank number. For each code you will find:

Always verify a code lookup against a second source when possible—cross-referencing two editions or databases catches typographical errors that could result in a non-functional key or a wasted blank.

Safety and Professional Responsibility

Key origination from code is a powerful skill that carries legal and ethical responsibility. You must verify customer authorization before originating or duplicating any key. Many states require a locksmith license before performing key origination services commercially—operating without that license is illegal regardless of technical skill. Retain job records including customer identification and authorization as required by your state licensing board.

When operating key-cutting machines: keep guards in place, wear safety glasses (metal filings are a cutting and eye hazard), and keep fingers clear of the cutter wheel. Secure key blanks properly in the machine clamp before cutting begins. If using a code machine with motorized components, follow lockout/tagout procedures during blade changes.

Key terms10

BittingA number representing the depth of a single cut on a key; the complete sequence of bitting numbers for all cut positions describes the key's code.
Depth incrementThe fixed vertical distance (in thousandths of an inch or millimeters) between successive bitting depth levels for a given lock system.
SpacingThe horizontal distance between cut positions, measured from a reference point (tip or shoulder) along the key blade.
Shear lineThe boundary between the rotating plug and the stationary shell of a pin-tumbler cylinder; correct key cuts align all pin stacks exactly at this line to allow rotation.
Maximum Adjacent Cut Specification (MACS)A manufacturer-defined rule stating the largest permissible difference in bitting depth between any two neighboring cut positions; bittings that exceed this value are mechanically invalid.
Key section (key profile)The cross-sectional shape of a key blade that determines which keyway it will enter; also called the keyway or key profile.
Theoretical bitting combinationsThe total number of mathematically possible bitting sequences for a key system, calculated as the number of depth levels raised to the power of the number of cut positions (D^P).
Key originationThe process of producing a working key from a code number without access to an existing key or the lock itself.
Driver pinThe upper pin in a pin-tumbler stack, pushed downward by a spring; it must be lifted to the shear line by the corresponding key cut for the cylinder to rotate.
Blank numberThe manufacturer's catalog designation for a specific key blank shape; it identifies the correct uncut key to use for a given keyway and lock series.

Worked examples4

1. A lock system has 5 cut positions and 6 depth levels (numbered 1–6). How many theoretical bitting combinations exist?
  1. Identify D (depth levels) = 6 and P (positions) = 5.
  2. Apply the formula: Total combinations = D^P = 6^5.
  3. Calculate: 6^1 = 6; 6^2 = 36; 6^3 = 216; 6^4 = 1,296; 6^5 = 7,776.
Answer: 7,776 theoretical bitting combinations.
2. A Schlage C keyway system has 10 depth levels (0–9) and 5 cut positions. How many theoretical bitting combinations exist?
  1. Identify D = 10 and P = 5.
  2. Apply the formula: Total combinations = D^P = 10^5.
  3. Calculate: 10^5 = 100,000.
Answer: 100,000 theoretical bitting combinations.
3. A manufacturer's spec sheet shows MACS = 4. A proposed bitting is 3-7-2-5-1. Identify any MACS violations.
  1. List adjacent pairs and compute absolute differences: |3−7| = 4; |7−2| = 5; |2−5| = 3; |5−1| = 4.
  2. Compare each difference to the MACS of 4: differences of 4 are exactly at the limit (acceptable); a difference of 5 exceeds the MACS.
  3. The pair at positions 2 and 3 (bitting values 7 and 2) produces a difference of 5, which violates MACS.
Answer: One MACS violation: the cut between positions 2 and 3 (7 to 2) has an adjacent difference of 5, which exceeds the MACS of 4. The bitting 3-7-2-5-1 is invalid.
4. A key system uses 4 cut positions and 5 depth levels (1–5) with a MACS of 3. Is the bitting 2-5-3-1 valid? How many theoretical combinations exist for this system?
  1. Calculate theoretical combinations: D^P = 5^4 = 625.
  2. Check MACS: |2−5| = 3 (acceptable, equals MACS); |5−3| = 2 (acceptable); |3−1| = 2 (acceptable).
  3. No adjacent difference exceeds 3, so no MACS violations are present.
Answer: The system has 625 theoretical bitting combinations. The bitting 2-5-3-1 is valid — no adjacent cut difference exceeds the MACS of 3.

The math in this lesson2

Learners evaluate powers of depth levels to count key combinations under MACS rules.
8.EE.1S-CP.9
In class: Lecture and guided notes on how lock manufacturers assign bitting depths, spacing increments, and key sections; students label a cross-section diagram of a pin-tumbler cylinder showing shear line, driver pins, and key cuts. · Worksheet drill: given five keyway families (e.g., Kwikset, Schlage C, Best A, Arrow, Master No. 3), students calculate the number of theoretical bitting combinations, identify MACS violations in a list of 20 bittings, and rank cuts from shallowest to deepest. · Small-group exercise using published code books (Ilco/Kaba key code reference or equivalent) to look up five residential key codes and record the bitting, blank number, and keyway for each, then verify entries against a second source.
Materials: Manufacturer depth-and-space specification sheets, current edition of a standard key code reference (e.g., Ilco Key Blank Reference or Kaba Ilco Key Code Manual), scientific calculators, graph paper, whiteboard
Check: Completed worksheet graded by instructor; students must correctly solve at least 90% of bitting calculations and flag all MACS violations to pass.

Practice check8

Answer each question, then check it. Nothing is recorded; this is your own practice.

Key origination and bitting mathematics
1. A pin-tumbler lock system has 6 cut positions and 5 depth levels. What is the total number of theoretical bitting combinations?
Key origination and bitting mathematics
2. A manufacturer specifies a MACS of 4. A bitting reads 1-6-2-5-3. Which adjacent pair, if any, is a MACS violation?
Key origination and bitting mathematics
3. What is the primary mechanical reason manufacturers impose a MACS rule?
Pin-tumbler cylinder theory
4. In a pin-tumbler cylinder, what condition must be met for the plug to rotate freely?
Key origination professional practice
5. When originating a key from a published code, why is it important to verify the bitting against a second source?
Legal and professional responsibility
6. A locksmith is asked to originate a key from code for a residential customer. Before cutting, what is the most critical non-technical step?
Key origination and bitting mathematics
7. A key system uses depth levels numbered 0 through 9 and has 6 cut positions. How many theoretical bitting combinations are possible?
Shop safety
8. Which personal protective equipment is most important when operating a motorized key-cutting machine?
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