Find the Delivery Floor Hidden in a Project’s Dependencies — Free
A list of task lengths hides the work that must wait for other work. Enter durations and predecessor names to expose earliest starts, earliest finishes and the longest dependency chain before promising a delivery day.
The proof surface
A first-30-days onboarding plan arranges goals. This route computes dependency timing for a defined project: parallel branches do not get summed, missing predecessors and cycles are rejected, and zero-float tasks are named without guessing staff availability.
Inputtask | duration workdays | predecessor labels, or -; planned delivery window in workdays from day zero
Rare deviceA first-30-days onboarding plan arranges goals. This route computes dependency timing for a defined project: parallel branches do not get summed, missing predecessors and cycles are rejected, and zero-float tasks are named without guessing staff availability.
Output artifactEarliest possible project finish 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: Brief | 2 | -; Prototype | 5 | Brief; Review | 3 | Prototype; Access audit | 4 | Brief. Planned delivery window in workdays from day zero = 12. Earliest possible project finish: 10 workdays. All records are invented.
Before using the dependency-rung route
Start with a small deliverable whose handoffs you understand: a portfolio prototype, internal process update or team training artifact. Give tasks stable short labels, then ask each owner what must be finished before their task can begin. A dependency is not merely a preference for doing one thing first. If a review truly needs the prototype, connect it; if research and layout can proceed independently, do not manufacture a link between them. Duration means elapsed working time in this model, not a count of person-hours. The output is a lower bound under unconstrained parallel resources, not a project promise. Keeping that distinction visible makes the result useful in a planning conversation without turning an arithmetic route into a staffing forecast.
Why the flat version breaks
Summing branches that can overlap
Fourteen total task-days can contain a ten-day path. Sum describes effort only under another staffing model; the longest dependent route describes this model’s elapsed floor.
Treating no predecessor as no work
A starting task still consumes its entered duration. Use a zero only for an explicit milestone, never as shorthand for an estimate nobody has provided.
Calling zero float an employee rating
Zero float is a property of the dependency model, not of a person’s performance. Calendars, shared staff and changing scope can create a different real critical path.
How to work the dependency-rung route
Name real handoffs
Use one stable label per task and copy predecessor labels exactly, separating multiple predecessors with commas. A dash means no predecessor. Labels are matched without case differences, but each task must remain unique. Keep client names, confidential milestones and internal identifiers out of shared examples.
Choose one duration convention
Use workdays throughout and allow fractions only when your estimates use them. A task begins after every predecessor finishes; the latest predecessor controls its start. Holidays, weekends, fixed bookings, travel and competing assignments are not represented by these abstract day numbers.
Trace the longest route
Earliest start is the maximum predecessor finish, or zero for a starting task. Finish equals start plus duration. The delivery floor is the maximum finish across tasks. A backward pass from that floor identifies zero-float tasks; their row notes show why shortening another branch may not help.
Take the floor to the owner
Compare the longest route with your entered delivery window, then discuss missing dependencies and resource conflicts with the project owner. A cyclic route cannot be scheduled by this method and is rejected with the affected label. Do not remove a genuine handoff merely to make the date look better.
What the dependency-rung route separates
Question
Before
Inspect this instead
Summing branches that can overlap
Fourteen total task-days can contain a ten-day path. Sum describes effort only under another staffing model; the longest dependent route describes this model’s elapsed floor.
Choose one duration convention
Treating no predecessor as no work
A starting task still consumes its entered duration. Use a zero only for an explicit milestone, never as shorthand for an estimate nobody has provided.
Trace the longest route
Calling zero float an employee rating
Zero float is a property of the dependency model, not of a person’s performance. Calendars, shared staff and changing scope can create a different real critical path.
Take the floor to the owner
This dependency-rung route replaces a manual count or calculation, not source verification or the responsible person’s review.
Run it on the samples, right here
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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.
Dependency arithmetic only, not a delivery guarantee, staffing recommendation or employment assessment. It assumes unlimited parallel resources and omits calendars, uncertainty and fixed constraints. Confirm the route and available people with the project owner before making a commitment; do not use it to judge workers.
Data note: The dependency-rung route processes task | duration workdays | predecessor labels, or - 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 climbing rung ladder
The article demo above runs without limits. The companion app keeps a local history, exports the rows as CSV, prints the dependency-rung route 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 dependency-rung route 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.
Dependency arithmetic only, not a delivery guarantee, staffing recommendation or employment assessment. It assumes unlimited parallel resources and omits calendars, uncertainty and fixed constraints. Confirm the route and available people with the project owner before making a commitment; do not use it to judge workers.
What this is built on
Method: Earliest start is the maximum predecessor finish, or zero for a starting task. Finish equals start plus duration. The delivery floor is the maximum finish across tasks. A backward pass from that floor identifies zero-float tasks; their row notes show why shortening another branch may not help.
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: task lengths hid which handoff controlled the finish. After: the longest dependent route and each task’s float are visible, while resource constraints remain a separate question.
Setting: Planned delivery window in workdays from day zero = 12. Expected summary: 10 workdays.
Brief finishes at day two. Prototype cannot start before that finish, so it reaches day seven; Review reaches day ten. Access audit branches from Brief and ends at day six. Adding all four durations gives fourteen, but fourteen is not the delivery floor when the two branches can run together. The longest dependency chain is Brief → Prototype → Review, ten workdays. Against a twelve-workday window, that model has two days of margin, before any resource or calendar constraint.
Setting: Planned delivery window in workdays from day zero = 12. Expected summary: 13 workdays.
Only Prototype changes, from five to eight workdays. The longest chain now finishes on day thirteen, one day beyond the same twelve-day window. Cutting Access audit by a day would not move that finish while it remains off the longest chain. That is the reason to expose dependencies rather than simply sort tasks by duration. A real team may nevertheless need the same person for both branches; this model does not grant permission to book simultaneous work.
Setting: Planned delivery window in workdays from day zero = 12. Expected summary: 0 workdays.
A zero-duration checkpoint followed by another zero-duration marker finishes at day zero. Both are valid milestones, not missing estimates silently converted to zero. By contrast, a blank duration is rejected. The edge case also separates a milestone from a task with actual effort: entering zero for an unestimated task would make the route falsely short. Keep unestimated work outside the numeric model until its owner supplies an explicit duration.
Optional AI formatting, never the calculation
Manual entry completes this dependency-rung route 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 dependency-rung route. Return strict JSON shaped as {"rows": [{"label": "string", "cells": ["string", "string"]}], "setting": "string"}. The columns are task | duration workdays | predecessor labels, or -; the setting is Planned delivery window in workdays from day zero. 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.