Build an Exact Cash Envelope From the Denominations You Have — Free
A cash budget does not tell you whether the actual notes can make an exact payment. Enter denomination values and available counts to assemble an exact amount with the fewest pieces, or expose the highest reachable amount below it.
The proof surface
Cash-versus-card tools divide a spending budget by payment method. This packet solves a finite denomination problem: counts constrain every choice, overpayment is never used, and an impossible exact amount stays visibly incomplete.
Inputdenomination label | value in minor units | pieces available; payment target in whole minor units
Rare deviceCash-versus-card tools divide a spending budget by payment method. This packet solves a finite denomination problem: counts constrain every choice, overpayment is never used, and an impossible exact amount stays visibly incomplete.
Output artifactCash reachable without overpayment with row-by-row context
Cost$0 local calculation · no card, paid key, subscription or signup · proposed filing price is not for sale
Sample, not your facts: Illustrative inputs: Fifty note | 5000 | 1; Twenty note | 2000 | 2; Ten note | 1000 | 3. Payment target in whole minor units = 6000. Cash reachable without overpayment: 6000 minor units assembled. All records are invented.
Before using the denomination-envelope packet
Use this for a known small payment with a confirmed currency and amount, not for carrying large cash balances or deciding what travel payment method is safest. Convert all denominations and the target to integer minor units before entry so decimal rounding cannot invent a coin. Different currencies must never be combined in one packet. The recipient’s acceptance policy, change availability, transaction limits and security arrangements are outside the calculation. The bounded search uses only the pieces you say are on hand and looks for a minimum-piece exact envelope. If exact payment is impossible, it finds the largest reachable amount below the target and then minimizes pieces at that amount. That distinction is useful because “closest” must not quietly mean paying too much.
Why the flat version breaks
Mixing major units and minor units
A value of 50 and a value of 5000 cannot both represent the same fifty-unit note in one calculation. Choose a single integer scale first.
Ignoring stock while making change
An unlimited-coin calculator can propose pieces you do not hold. This envelope respects each count and exposes the gap when finite stock blocks an exact payment.
Treating closest-below as paid
The partial result is an amount you can assemble, not the amount owed. The remaining gap still needs an accepted payment arrangement.
How to work the denomination-envelope packet
Confirm one currency and minor unit
Use integer values such as 500 for a five-unit note only when that currency uses one hundred minor units per major unit. The app does not fetch exchange rates or decide the currency scale. Keep actual cash-storage locations out of row labels.
Count the physical inventory
Each denomination has a positive value and a non-negative whole count. Enter a denomination value once, even if notes are in two pockets; combine those counts yourself. This avoids pretending duplicate rows are separate kinds of currency.
Read exact versus partial
A bounded change-making search never exceeds an available count or the target. Among exact solutions it selects the fewest pieces. If there is no exact solution, the headline shows the largest attainable amount below target and the row notes disclose the remaining gap.
Recount before handing over
The selected pieces are a proposed assembly from your entries, not a payment or money transfer. Check acceptance and the actual notes with the provider. Do not use a partial reading as evidence that a bill was settled.
What the denomination-envelope packet separates
Question
Before
Inspect this instead
Mixing major units and minor units
A value of 50 and a value of 5000 cannot both represent the same fifty-unit note in one calculation. Choose a single integer scale first.
Count the physical inventory
Ignoring stock while making change
An unlimited-coin calculator can propose pieces you do not hold. This envelope respects each count and exposes the gap when finite stock blocks an exact payment.
Read exact versus partial
Treating closest-below as paid
The partial result is an amount you can assemble, not the amount owed. The remaining gap still needs an accepted payment arrangement.
Recount before handing over
This denomination-envelope packet replaces a manual count or calculation, not source verification or the responsible person’s review.
Run it on the samples, right here
FIRST-LOAD
HYPOTHESIS / PROTOTYPE — checkout unavailable. Calculation is local. A draft is saved automatically in this browser profile when storage is available; Reset to sample clears it. Optional Pro history stores only five summaries and has its own deletion control. State links encode your inputs and can remain in browser history, clipboard or recipients’ records; share only non-sensitive rows. Optional external AI formatting leaves this device. The required site analytics beacon reports page activity; shared URLs contain encoded inputs. Do not treat an encoded URL as private. The calculator has no input-collection endpoint.
Finite-denomination arithmetic only, not financial, travel-security or currency-exchange advice. It does not transfer money, verify cash authenticity or confirm a recipient’s acceptance rules. Verify the currency, amount and accepted denominations with the provider; arrange another payment method when the packet is partial and avoid sharing sensitive cash details.
Data note: The denomination-envelope packet processes denomination label | value in minor units | pieces available locally. Starter/sample selection and Run compute in this tab; no input is sent by the calculator. A local draft may be saved; explicit state-link sharing or optional external AI formatting can disclose inputs. Use non-sensitive labels.
Go deeper: the companion app files the same reading as a stapled evidence packet
The article demo above runs without limits. The companion app keeps a local history, exports the rows as CSV, prints the denomination-envelope packet reading, and holds your drafts on this device — one complete free app run; the proposed $4 one-time filing layer is not for sale.
The denomination-envelope packet answer stays complete for free. The proposed $4 one-time filing layer adds row CSV, print and five local reading summaries, not hidden answers. Checkout is unavailable; the article demo remains unlimited.
Finite-denomination arithmetic only, not financial, travel-security or currency-exchange advice. It does not transfer money, verify cash authenticity or confirm a recipient’s acceptance rules. Verify the currency, amount and accepted denominations with the provider; arrange another payment method when the packet is partial and avoid sharing sensitive cash details.
What this is built on
Method: A bounded change-making search never exceeds an available count or the target. Among exact solutions it selects the fewest pieces. If there is no exact solution, the headline shows the largest attainable amount below target and the row notes disclose the remaining gap.
All sample records, dates, quantities and labels are invented. No outside policy, contract, rate, clock offset, measurement or accessibility standard is represented as verified.
Google’s official pricing documentation, fetched 2026-09-30, says AI Studio is free in available regions. Optional formatting may require a Google account; manual local entry requires none. Limits can change and free-tier content may be used to improve products. Do not send private records.
Before: a cash total did not establish an exact set of notes. After: available counts constrain the selected envelope and an impossible exact payment stays partial.
Setting: Payment target in whole minor units = 6000. Expected summary: 6000 minor units assembled.
One 5,000-unit note plus one 1,000-unit note reaches the 6,000-unit target with two pieces. The available twenties do not need to be used. All values belong to one currency and its minor-unit convention; if the convention is one hundred minor units per major unit, these are fifty and ten. The algorithm minimizes pieces among exact solutions. It never assumes the recipient can provide change or that a particular denomination is accepted at a destination.
Sample B — changed plan
Twenty note | 2000 | 2
Five note | 500 | 3
Setting: Payment target in whole minor units = 6000. Expected summary: 5500 minor units assembled.
With only two twenties and three fives, the most available cash below the target is 5,500 units: four thousand plus fifteen hundred. The remaining gap is five hundred. No exact envelope exists from those counts, so the result is explicitly marked partial rather than rounded up or silently borrowing another note. A partial envelope is not a completed payment. Obtain the missing accepted denomination or ask the provider about another payment method before relying on it.
Sample C — boundary convention
Two-thousand note | 2000 | 3
Small coin not held | 50 | 0
Setting: Payment target in whole minor units = 6000. Expected summary: 6000 minor units assembled.
Three 2,000-unit notes exactly reach the target. A zero count for the fifty-unit coin is a deliberate statement that none is available; it contributes nothing. The smallest-piece tie rule is deterministic, but an alternative equally small combination can exist in other inventories. The printed or copied packet lists the selected pieces, not every piece in the wallet, so compare those selected counts with the physical cash before sealing an envelope.
Optional AI formatting, never the calculation
Manual entry completes this denomination-envelope packet for free without signup. If available to you, the free AI Studio interface linked in the sources may format fictional or non-sensitive notes; external access may require an account. No API key or AI call is built into this tool. Free-tier content may be used to improve products. Review each cell and transcribe it to the labeled row schema; do not paste the JSON object into the row box.
Format only these fictional or non-sensitive notes for a denomination-envelope packet. Return strict JSON shaped as {"rows": [{"label": "string", "cells": ["string", "string"]}], "setting": "string"}. The columns are denomination label | value in minor units | pieces available; the setting is Payment target in whole minor units. Keep all supplied strings and quantities exactly; do not calculate, infer missing entries, invent dates or add advice. If any required value is missing, return an empty rows array and ask me for it separately. I will verify every cell against my source and manually transcribe rows using vertical bars before running the local calculator.
An AI response is not executed, fetched or trusted as a result. Missing values remain questions; the strict local parser checks the rows you actually enter.