Split a total amount across a ladder of rungs that grow or shrink by a fixed percentage step, using the finite geometric series formula to size every rung exactly.
Quick Facts
Method
Finite geometric series
Rung k = Rung 1 × (1 + step%)^(k−1); every rung's amount sums back exactly to your total.
Results
Calculated
Rung 1 (base)
—
Smallest allocation, at the bottom of the ladder
Top rung
—
Largest allocation, at the top of the ladder
Top ÷ base ratio
—
How many times larger the top rung is than the base rung
Average per rung
—
Total ÷ number of rungs, for comparison
Ready
Set the total amount, rung count, and step percent, then press Calculate.
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How to use this calculator
This calculator splits a total amount into an allocation ladder: a series of rungs, from a base amount up to a top amount, where each rung is a fixed percentage larger or smaller than the one before it. Enter the total amount, the number of rungs, and the step percent, then click Calculate to see the base rung, the top rung, the spread between them, and the plain average for comparison. Click Clear to reset all fields to the defaults.
Understanding the inputs
Total amount to allocate is the full dollar amount being spread across the ladder. Number of rungs is how many steps the ladder has — a 5-rung ladder has a base rung, a top rung, and three in between. Step change per rung is the fixed percent each rung grows (a positive number) or shrinks (a negative number) compared with the rung directly below it. A step of 0% produces a flat ladder where every rung gets an equal share.
Interpreting the results
Rung 1 (base) and Top rung are the smallest and largest allocations in the ladder — solved from the finite geometric series formula so that all rungs sum back exactly to your total. Top ÷ base ratio shows how much larger the top rung is than the base rung — a ratio of 1.00× means a flat ladder, and anything above 1.00× means the ladder grows toward the top. Average per rung is the plain total divided by the rung count, useful for comparing the base and top rungs against a simple equal split.
Frequently Asked Questions
What is an allocation ladder?
An allocation ladder splits a total amount into a series of rungs where each rung is a fixed percent larger or smaller than the one before it. It follows the finite geometric series formula and is used for staggered budgets, tiered payouts, bond and CD laddering, and step-up or step-down savings plans.
How is the base rung (Rung 1) calculated?
Rung 1 is found by solving the geometric series sum for its first term: Rung 1 = Total × (r − 1) / (r^n − 1), where r = 1 + step percent ÷ 100 and n is the number of rungs. Every later rung equals the previous rung multiplied by r.
What happens with a 0% step?
A 0% step produces a flat ladder: every rung receives an equal share, Total divided by the number of rungs. That is identical to a plain equal split across all rungs.
Can the step percent be negative?
Yes. A negative step shrinks each rung relative to the last, front-loading the largest allocation at Rung 1 and tapering toward the top. The step percent must stay above −100% so the growth ratio stays positive.