PUM Calculator · step-ratio operations

Compute any ring's value at any sector. Pick a divisor D below; every mode uses it. Try D = 32 first — that's the chart's default outer-ring resolution.

— half / default / double resolution

Orientation

The PUM mandala arranges 24 numerical systems as concentric rings. Each ring has an anchor value (its MAX — e.g. 24 for hours, 360 for degrees, 25,920 for the great-year cycle) and is swept clockwise from 12 o'clock in equal steps. Sector S of a linear ring evaluates to MAX × S / D.

Reading a ring
  • S runs 0 .. D−1 clockwise from 12 o'clock. S = D/4, D/2, 3D/4 land on the cardinal clock positions.
  • Linear rings: value = MAX × S / D. Clock at D = 32: S = 8 → 6 hrs, S = 16 → 12 hrs.
  • S = 0 holds MAX itself (cycle wrap-around anchor), not zero.
  • Native sector counts on the chart: 16 for §2–§10, 32 for §11–§24. The D toggle re-resolves any ring at 16 / 32 / 64.
  • Two rings ignore D: §19 uses the n × 10/9 dimension ladder, §24 uses 10S × (36/D).
Modes
  • ① apply S/D to a value V — table of every cell for a hypothetical ring with MAX = V.
  • ② fix S, show the value in every ring.
  • ③ reverse — given a value, the closest sector in each ring.
  • ④ reference table — MAX, step size, formula.
Categories
aether light / 6D / DC · sun solar radii, orbital miles · time hours, years, cycles · matter 64/0 cycle, mileages, plasmoid rotations · freq elemental frequencies, sound, RFEU, dimensions · degrees compass, language · special non-linear (§19, §24)

① Apply step ratio · V × S/32

V is the MAX of a hypothetical ring; the table lists every cell at the current D. Try 24 (clock), 360 (compass), 144 (light), 25,920 (great year), 1,296 (RFEU).

② Sector → Values across all rings · cell(S, ring) = maxring × S/32

Fix S, see every ring at that angular position. S = D/4, D/2, 3D/4 land on 3 / 6 / 9 o'clock. At S = 16, D = 32 (bottom of chart): clock 12 hrs, compass 180°, light 72, dimensions 17.78.

/ 32 = 0.500 × max

③ Value → which sector?

Reverse: per ring, the sector closest to the entered value. Fractional sector counts shown so you can see if it lands on a boundary or between cells. Try 432, 144, 25,920, 1,296, 7,200.

④ Reference · all rings at 32 steps

Per-ring formula strings quote the chart-native D = 32; the computed values above them always use the selected D.

MAX, step size at the current D, formula. §19 ladder: sec 1 = 1.111, sec 9 = 9.999, then continues × 10/9. §24 exponential: 10S × (36/D) — at D = 32, sec 16 = 10¹⁸, sec 32 = 10³⁶.

§RingMax One step (= max / D)Formula
Glossary — the terms used on this page
Mandala
Sanskrit for "circle". In PUM, the chart is a series of concentric ring-bands around a central core, with each ring representing one numerical system.
Ring
One of the 24 concentric bands. Numbered §1 (centre: Sun/Earth/Moon) outward to §24 (outermost: All Plasmoid Energy).
Sector / Cell
A wedge-shaped slice of a ring. Sectors are numbered 0..D−1 going clockwise from 12 o'clock. A "cell" is the ring × sector intersection.
MAX (anchor value)
Each ring has one characteristic number — its largest meaningful value (e.g. 24 hours, 360°, 25,920 years for the great year). At sector 0 the ring shows MAX as a "wrap-around" anchor; at sector D it would also equal MAX (the cycle closes).
Divisor D
How many equal steps the ring is split into. The chart uses 16 for inner rings, 32 for outer, but any ring can be re-divided by any D. This calculator lets you switch among 16, 32, and 64.
Step ratio (S/D)
The fractional position of sector S within the ring. The value at that sector is MAX × S / D for linear-sweep rings.
Ladder
A non-linear ring whose values follow a fixed step like × 10/9 (used for §19 Dimensions). The ladder ignores D — sector S = S × 10/9 always.
Exponential ring
§24 All Plasmoid Energy uses 10S × (36/D). The exponent grows linearly with S while the value grows exponentially.