Add branch airflows to find trunk flow and size sections at a chosen velocity.
Concepts behind this calculation
Aggregate downstream terminal demands through a complete branch tree for two stated operating conditions, then derive theoretical per-segment clear sizes from project target velocities. Retain simple three-branch arithmetic checks.
A trunk carries the simultaneous demand of its downstream terminals. The largest terminal demand from each of two alternative operating states cannot be added as though those peaks occurred together.
Tree aggregation follows connectivity rather than the order of rows. Every leaf demand must belong to the documented tree; a missing terminal understates all of its upstream segment flows.
How to use this calculator
For a three-branch check enter Branch A, Branch B and Branch C airflow; add Parent duct airflow for continuity comparison or Selected trunk target velocity for sizing.
For the complete tree document both state descriptions and actual airflow direction, then enter the complete segment tree with parent/child connectivity and per-segment velocity targets.
List every leaf in the leaf-demand table with State A and State B CFM. Confirm the simultaneous-state basis, then inspect upstream aggregation and each segment size.
Calculation method and applicability
For each stated condition, Qsegment = sum of descendant leaf demands. Qdesign = max(sum in A, sum in B), not sum of terminal maxima. Required area = Qdesign/Vtarget; derive round, rectangular or flat-oval clear geometry.
Qsegment and Qdesign = segment and governing simultaneous airflow (CFM); A = required clear area (ft²); Vtarget = selected segment velocity (FPM). States A and B are alternative complete demand conditions.
Input definitions and units
Branch calculation
The tree method sums each complete supplied state separately; it does not solve actual pressure-driven flow or infer diversity. Simple three-branch checks remain selectable. Choices: Complete branch tree — stated flows and per-segment velocity sizes; Sum three branch airflows; Compare parent CFM with three branches; Sum branches and estimate a round trunk by target velocity.
Branch A airflow (CFM)
Design airflow at this branch. Applies to Branch calculation: Sum three branch airflows or Compare parent CFM with three branches or Sum branches and estimate a round trunk by target velocity.
Branch B airflow (CFM)
Design airflow at this branch. Applies to Branch calculation: Sum three branch airflows or Compare parent CFM with three branches or Sum branches and estimate a round trunk by target velocity.
Branch C airflow (CFM)
Design airflow at this branch. Applies to Branch calculation: Sum three branch airflows or Compare parent CFM with three branches or Sum branches and estimate a round trunk by target velocity.
Parent duct airflow (CFM)
For the comparison mode only. Applies to Branch calculation: Compare parent CFM with three branches.
Selected trunk target velocity (FPM)
A user-selected target; pressure loss and fitting effects are not included. Applies to Branch calculation: Sum branches and estimate a round trunk by target velocity.
Complete tree and flow-reference basis
Identify the actual branch drawing, all terminal leaves, airflow-reference conditions and independently established whole-system operating envelope. The two supplied states do not prove coverage of all possible zoned combinations. Applies to Branch calculation: Complete branch tree — stated flows and per-segment velocity sizes.
State A description and demand basis
Name the complete simultaneous state, such as the project heating design condition, and identify how terminal demands were established. Room loads and temperature differences are not calculated here. Applies to Branch calculation: Complete branch tree — stated flows and per-segment velocity sizes.
State B description and demand basis
Name the second complete state, such as project cooling design. For only one supplied condition, enter zero for every State B flow and explicitly describe State B as inactive. Applies to Branch calculation: Complete branch tree — stated flows and per-segment velocity sizes.
Topology and simultaneous-state applicability
Confirm a complete connected tree, every actual leaf, two simultaneous schedules on one compatible flow basis and actual target-velocity/shape criteria. No automatic density conversion, diversity factor or unlisted operating state is added. Choices: Not established; Complete tree, terminal/state demands and design criteria established. Applies to Branch calculation: Complete branch tree — stated flows and per-segment velocity sizes.
Actual airflow direction
Parent nodes are closer to root 0 in both cases. Supply air follows parent to child; return/intake flow follows child to parent. Numbering does not assert a fan pressure plane or installed common trunk. Choices: Supply — flow away from root; Return/intake — flow toward root. Applies to Branch calculation: Complete branch tree — stated flows and per-segment velocity sizes.
Complete segment tree and velocity targets (ID, parent, child, target FPM, shape, aspect)
No header. Unique segment IDs and node IDs 1–10000; root parent 0; every nonroot node has one parent. Positive project target velocity per segment. Shape 0=round with aspect 0; 1=rectangle or 2=flat oval with width/height (major/minor) ratio at least 1. No loops, merged paths or internal-node terminal flows. At most 100 segments. Applies to Branch calculation: Complete branch tree — stated flows and per-segment velocity sizes.
All leaf demands in the two stated conditions (leaf node, State A CFM, State B CFM)
No header. Exactly one row for every leaf, no duplicate or internal nodes. Each state flow is finite and nonnegative; each terminal needs positive demand in at least one condition. Do not mix different simultaneous states within a column or incompatible actual/standard/test CFM. At most 100 terminal rows. Applies to Branch calculation: Complete branch tree — stated flows and per-segment velocity sizes.
How to interpret the result
Use the per-state segment totals to check continuity and the design-flow column to size each segment. Treat required area as a velocity target, with resistance and balancing still to be assessed.
Worked examples
Complete branch tree — stated flows and per-segment velocity sizes
Inputs: Constructed four-terminal tree. State A demands at nodes 3, 4, 6 and 7 are 250, 150, 100 and 100 CFM; State B demands are 150, 250, 200 and 50 CFM. Each column is one complete simultaneous condition. Seven listed sections use explicit target velocities and theoretical shape criteria.
Calculation: Root State A flow is 600 CFM and State B is 650 CFM, so the larger stated requirement is 650 CFM. Segment 2 serves nodes 3 and 4: both state sums are 400 CFM, even though the sum of those terminals’ separate maxima is 500 CFM. The main round section at a selected 700 FPM needs area 650 / 700 ft².
Result: The theoretical main diameter is 13.048000 in. Summing all terminal maxima gives 800 CFM, which is not either supplied root condition. Different segments can have different controlling states; their maxima do not form one simultaneous solved state. Additional operating combinations, actual nominal sizes and pressure budgets require separate assessment.
Sum three branch airflows
Inputs: Branches 250, 150 and 100 CFM.
Calculation: Add the listed branch airflows.
Result: Parent airflow 500 CFM.
Compare parent CFM with three branches
Inputs: Parent 500 CFM; branches 250, 150 and 100 CFM.
Calculation: Parent minus listed branches.
Result: 0 CFM arithmetic difference.
Sum branches and estimate a round trunk by target velocity
Inputs: Branches 250, 150 and 100 CFM at selected 700 FPM.
Calculation: Sum 500 CFM and solve the round area.
The three simple methods retain exactly three branch inputs. The tree method covers only the complete supplied terminal/state schedules. No diversity, leakage, density conversion or simultaneous-use factor is inferred.
All generated sizes are theoretical target-velocity clear geometry, not a solved equal-friction network, nominal stock schedule, actual pressure-driven distribution or full Manual D design.
Branch arithmetic does not confirm measured balancing or allowable room-to-room pressure.
Each stated condition is summed separately before choosing a per-segment maximum. The sum of individual terminal peaks is a diagnostic, not the selected root duty. Per-section maxima need not occur together, and an unrepresented zoned combination can govern.
All actual leaf demands must be present in one connected tree. Root 0 can connect to several sections and does not create an unlisted physical common trunk. Loops, merging paths and internal-node extraction need a different schedule.
The actual operating-state envelope, low-speed applicability, source demands, flow-reference basis and chosen target velocities require independent support. Installed clearances, component losses, noise and structural/current-code approval remain separate.
FAQs
Why is the trunk design flow below the sum of terminal maxima?
The tree evaluates complete State A and State B separately, then selects the larger segment total. Terminal peaks from different states may not be simultaneous.
Does a branch total predict how air divides?
No. It adds stated demands. Actual flow division requires resistance, pressure boundaries and fan behavior; velocity-derived geometry alone does not balance the network.
Sources
ASHRAE 2025 Fundamentals: Duct DesignContinuity, Q=VA and section-design context. Per-state descendant summation is explicitly derived tree arithmetic; no implied diversity or full Manual D selection.
ACCA Manual D informationOfficial residential duct-design scope. This arithmetic/velocity schedule does not reproduce or certify the complete manual.
RESNET 2014 HVAC Verifier Student GuidePrinted/physical page 38 branch-removal flow example was read and visually inspected through the web PDF tool, while direct requests returned 403. Only 525/266/86/81/36/56 CFM arithmetic is reproduced; its heuristic size/velocity recommendations are not imposed.
