A rotating-disc cylinder uses separate gated discs and a locking sidebar. Normal key operation aligns the gates so the sidebar can move inward and the plug can turn. This generic cutaway illustrates that sequence. The calculator compares nominal code counts and an ideal angular-clearance allowance.
Disc Tumbler Lock Interactive Calculator
Explore normal disc alignment and sidebar release with an illustrative inserted key. Compare nominal code-space estimates separately from the common angular-error check.
Equation Used
- Independent nominal code positions before applying estimated usable fraction.
- Integer position/disc counts.
- Common residual angular error.
- Ideal angular fit only.
Generic geometry and combinatorics. No manufacturer keying capacity, attack-resistance rating or complete release test.
The plug waits for the sidebar
The exploded view shows every entered disc, an inserted key, the peripheral gates, a continuous sidebar and the housing envelope. The individual discs approach alignment during a prescribed representative key-turn sequence. The sidebar moves inward before the plug turns.
On the return part of the cycle, the plug comes back first, the bar returns to its housing position and the discs return to their initial positions. If the entered residual error exceeds the allowance, the sidebar remains out and the plug stays still.
Disc spacing is enlarged for visibility. Key contact timing and displayed code assignments are illustrative. The drawing does not reproduce proprietary key cuts, return-bar details or the complete construction of a named cylinder.
Two separate comparisons
The first calculation is a nominal code-space estimate based on independent disc positions. The usable fraction is the user’s assumption; it does not implement a manufacturer’s master-key restrictions, excluded combinations or key-profile system.
The second calculation compares a common residual angular error with an entered clearance allowance. It is an ideal angular fit check, not a real-world lock-release test. Radial dimensions, individual-disc errors, tolerances, wear and additional blocking features are not solved.
Count estimate and angular margin
For n discs, a nominal positions per disc and usable fraction f, the estimated integer count is floor(aⁿf). Integer arithmetic is used to avoid rounding the largest position/disc combinations before the usable fraction is applied.
The result and animation display the full estimated integer count. The logarithmic comparison is log₂(count), not an attack-resistance score.
Angular margin is allowance−|residual error|. A nonnegative margin means the ideal angles fit, including a zero-clearance boundary in this simplified model. It does not guarantee mechanical release. The separate gate-detail angles are enlarged 20 times and explicitly labeled.
Ten discs with nine nominal positions
The default example has 9¹⁰ nominal assignments and a 56.5% entered usable fraction. The integer estimate is shown in full beside the animation, with its logarithmic comparison below.
The default 0.5° residual error and 0.5° allowance give zero angular margin. Raising the error above the allowance keeps the bar out and prevents the illustrated plug turn.
With four discs, four positions and 20% usable fraction, the estimate is floor(256×0.20)=51. The result displays all 51 estimated usable codes.
Code space does not establish security performance
The nominal count assumes independently selectable positions and an estimated fraction. It does not account for manufacturing constraints, key distribution, physical attack resistance, key control, authorization systems or certified performance.
The animation is for normal key operation and geometric explanation. Its clearances and input ranges are not production specifications for any commercial lock. For a particular lock, use its manufacturer’s keying information and independently established performance ratings.
Rotating-disc cylinder questions
Why can the key move while the plug stays still?
The discs first need to align their gates with the sidebar. The plug is held until the modeled sidebar can move inward.
Is the full count a manufacturer keying capacity?
No. It is the integer estimate from the selected n, a and f.
Are the reported bits a security rating?
No. They are the base-two logarithm of that count. Actual security depends on much more than combinatorics.
Does zero angular margin guarantee opening?
No. It is an ideal boundary without additional dimensional, frictional or blocking constraints.
References
- ASSA ABLOY CL100 cam lock description — normal key alignment of disc gates permits the locking bar to disengage the cylinder from its housing.
- ABLOY key-systems brochure — rotating-disc cylinder family and component principle. The generic calculator inputs do not represent that manufacturer’s complete keying system.
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