Master Key System Calculator
Key bitting calculation for master and sub-master groups.
About this calculator
This calculator estimates how many usable key combinations a pin-tumbler master key system can support, and what it will cost to cut it. It starts from the theoretical maximum bitting space — the number of available cut depths raised to the power of the pin positions — then narrows that down by MACS, the Maximum Adjacent Cut Specification that caps how much depth can differ between any two neighboring pins (cutters won't reliably run adjacent cuts steeper than that without weakening the key or binding the pins). The calculator counts every adjacent-depth pair that satisfies the MACS limit, turns that into a fraction of all possible pairs, and raises that fraction to the power of one less than the pin count to estimate how much of the full combination space actually survives the constraint.
Master keying then eats further into that usable space: each level of hierarchy (master, grand master, and so on) reserves pin splits, and the calculator models this as roughly halving capacity per level, while also estimating the count of "incidental keys" — unintended cross-keys that could open a lock they weren't meant to, which grows as 2^(levels) − 1. Cost is a flat per-lock keying charge plus a system design fee that jumps for three- or four-level hierarchies. Because the MACS reduction is an approximation (real bitting arrays also exclude sequences with too many same-depth or ascending/descending runs), treat the combination counts as planning estimates, not a guarantee any specific bitting array is available from your key blank supplier.
Inputs
Results
Total key combinations
1,000,000
How to Use This Calculator
- Enter the pin positions and depths per pin for your cylinder (e.g., 6 pins, 10 depths for Schlage).
- Set the MACS (Maximum Adjacent Cut Specification) to constrain valid adjacent-pin combinations.
- Set the number of master levels needed in the hierarchy (1 = master+change, up to 4 = great-grand master).
- Input the number of sub-master groups and the keys needed per group.
- Review the MACS-compliant combinations, available change keys, and incidental key risk to confirm the system is feasible.
- Check the capacity utilization and estimated cost before finalizing the keying schedule.
How the result changes with Pin positions
| Pin positions | Total key combinations |
|---|---|
| 4 | 10,000 |
| 4.5 | 100,000 |
| 7 | 10,000,000 |
What each input means
- Pin positions
- Number of pin chambers in the lock cylinder (typically 5 or 6).
- Depths per pin
- Number of available cut depths (e.g., Schlage = 10, Kwikset = 7).
- MACS
- Maximum Adjacent Cut Specification — max depth difference between neighboring pins.
- Master levels
- Hierarchy depth: 1 = master+change, 2 = grand master, 3 = great-grand master, 4 = max.
- Sub-master groups
- Number of sub-master groups (e.g., departments, floors, or zones).
- Keys per group
- Number of individual change keys needed in each sub-master group.
What each result means
- Total key combinations
- Theoretical maximum key bittings (depths^pins) before constraints.
- MACS-compliant combos
- Usable combinations after applying MACS constraint to adjacent pins.
- Available change keys
- Total unique change keys the system can support across all groups.
- Keys per group (max)
- Maximum unique change keys available per sub-master group.
- Incidental keys (risk)
- Estimated number of cross-keys that could unintentionally open other locks.
- Capacity used (%)
- Percentage of system capacity consumed by requested keys (keep under 100%).
- System feasible (1/0)
- 1 if the system can accommodate all requested keys, 0 if over capacity.
- Estimated cost
- Approximate cost including system design fee and per-lock keying charge.
How this is calculated
Worked example, using the default values
- Identify Input Parameters4 parametersPin positions = 6, Depths per pin = 10, MACS = 4, Master levels = 2 = 6 input(s) provided
- Calculate Total key combinationsTotal key combinations1000000 = 1000000
- Calculate MACS-compliant combosMACS-compliant combos168070 = 168070
- Calculate Available change keysAvailable change keys42016 = 42016
Engine last updated . Checked against 3 independently-derived tests — how we verify calculators. Built by Paul Gunder, a software engineer, not a licensed financial, medical, or legal professional.
Frequently Asked Questions
Why does raising the MACS number increase usable combinations?
MACS caps how far apart two adjacent pin depths can be, and the calculator counts every depth pair that satisfies that cap to build the survival fraction it raises to the pin-count power. A higher MACS allows more depth pairs to qualify — more valid combinations of adjacent cuts survive the filter — so the usable combination count grows. A lower MACS is stricter about adjacent-cut steepness and throws away a larger share of the theoretical bitting space.
Why does adding a master-key level cut my available change keys so sharply?
The calculator divides usable combinations by subMasterGroups times 2 raised to the number of master levels, so each additional hierarchy level halves the change keys available per sub-master group. Going from 1 level to 2 cuts capacity in half again, which is why grand-master or great-grand-master systems need noticeably deeper bitting arrays (more pins or more depths) to serve the same number of end users as a simple master system.
What are 'incidental keys' and why does that risk grow so fast at higher master levels?
Incidental keys are change keys that unintentionally open a lock they weren't meant to, a side effect of the pin splits master keying introduces. The calculator models this risk as 2^(master levels) − 1 extra openings per lock, so it doubles roughly with every added level: a 1-level system estimates 1 incidental opening per lock, while a 3-level system estimates 7. That's why complex hierarchies need careful keying schedules, not just more bitting depth.
Why did my estimated cost jump sharply when I increased master levels from 2 to 3?
The calculator uses a step function on masterLevels: at 2 levels or fewer, the design fee is $150 and the per-lock keying charge is $28, but at 3 or 4 levels both jump to $350 and $40 respectively. That reflects the added complexity of designing and cutting a great-grand-master or larger hierarchy, not a gradual per-level increase.
Related Calculators
The questions that sit next to this one — chosen by subject, including calculators filed under a different category.
More in Home, Garden & Maintenance.