TFA – Total Flow Area Calculator
Total flow area is the open area a fluid actually has to pass through: the cross-section of one duct or pipe, or the sum of several identical openings such as the nozzles on a drill bit. This calculator covers six shapes (circular, rectangular, square, elliptical, triangular, and a multiple-openings mode) plus a drilling-nozzle mode for mixed nozzle sizes in 32nds, applies an optional blockage factor, and reports gross area, net area, blocked area and flow efficiency. Enter your dimensions and the four numbers appear together.
Enter one number per nozzle, separated by commas. Mixed sizes are summed directly; there is no need to run one size at a time.
Areas are reported to 4 decimals and efficiency to 2 decimals. The calculator is unitless: enter inches and read square inches, enter centimeters and read square centimeters. It computes area only; it does not convert units or compute flow rates.
Quick Answer
Three identical 10/32-inch drill nozzles have a total flow area of 0.2301 in². Each nozzle’s area is π × (10÷32 ÷ 2)² = 0.0767 in², and three of them total 0.2301 in². Drillers cross-check this with the 32nds shortcut, (10² + 10² + 10²) ÷ 1303.8 = 0.2301 in². The Multiple mode is pre-filled with this exact example. Mixed sizes no longer need hand addition: Drilling Nozzles mode with 10, 10, 10, 12, 12 gives 0.4510 in² at 0% blockage.
Key takeaways
- Total flow area is the open area fluid can actually use: one duct’s cross-section, or the sum of identical openings.
- This calculator is unitless. Enter inches and read square inches, enter centimeters and read square centimeters; it never converts units.
- The Multiple mode handles identical openings. Mixed nozzle sizes use the Drilling Nozzles (32nds) mode, which sums each size squared over 1303.8 from the list you enter.
- Blockage factor models grilles, filters and fouling: net area = gross × (1 − blockage ÷ 100), and efficiency = 100 − blockage.
- The tool computes area, not flow rate. Area times velocity gives flow rate (Q = A × V), which is a separate calculation.
- Quick Answer
- How to use the TFA calculator
- Shapes, formulas and the drilling-nozzle mode
- Worked example: three 10/32-inch drill nozzles
- The driller’s 32nds shortcut, and mixed nozzle sizes
- What the blockage factor models
- Where drillers, HVAC designers and hydraulics engineers use TFA
- What competing calculators miss
- Frequently asked questions
- Add This Calculator to Your Website
- References
How to use the TFA calculator
Pick the shape, enter its dimensions, add any blockage, and read the four results. The fields stay hidden until you calculate, and the drill-nozzle example is pre-filled so pressing Calculate immediately shows 0.2301 in².
- Choose the shape type: Circular Pipe, Rectangular Duct, Square Duct, Elliptical Duct, Triangular Duct, or Multiple Pipes/Ducts for a set of identical openings. Only the inputs for the chosen shape are shown. For drilling nozzles, choose Drilling Nozzles (32nds) and enter the sizes as a comma-separated list, one number per nozzle.
- Enter the dimensions: full diameter for a circle, width and height for a rectangle, side for a square, the full major and minor axes for an ellipse, base and perpendicular height for a triangle. Every dimension must be a positive number.
- Set the blockage factor: the percent of the area blocked by screens, filters or buildup, from 0 to 100. Leave it at 0 for a clean opening.
- Click Calculate: the hero number shows the net flow area, with gross area, blocked area and flow efficiency in the four fields below. Use Copy my results or Share results to keep the figures.
Invalid inputs are rejected with a plain message: a missing or non-positive dimension (“Please enter a valid positive diameter.” and its siblings), or a blockage outside 0–100 (“Blockage factor must be between 0 and 100 percent.”).
Shapes, formulas and the drilling-nozzle mode
Each shape uses the standard geometric formula for its cross-section. The calculator works in your units, so a diameter of 10 means 10 of whatever unit you chose.
| Shape | Formula | Notes |
|---|---|---|
| Circular | A = π × (D ÷ 2)² | Enter the full diameter, not the radius. |
| Rectangular | A = W × H | The workhorse of HVAC duct sizing. |
| Square | A = S² | One side length is enough. |
| Elliptical | A = π × (a ÷ 2) × (b ÷ 2) | Enter the full axes a and b, not the semi-axes. |
| Triangular | A = ½ × B × H | H is the perpendicular height. |
| Multiple | TFA = N × Aunit | N identical openings of area Aunit; the drilling-nozzle mode. |
Then the blockage adjustment applies to whichever gross area the shape produced: blocked area = gross × blockage ÷ 100, net area = gross − blocked, and efficiency = net ÷ gross × 100. Areas print to 4 decimals, efficiency to 2.
Worked example: three 10/32-inch drill nozzles
Oilfield nozzle sizes are spoken in 32nds of an inch, so a “10” nozzle is 10/32 in. across. The Multiple mode is pre-filled with 3 units at 0.0767 in² each; press Calculate to reproduce this:
The same answer falls out of the rig-floor shortcut below, which is the point: the tool and the shortcut agree to four decimals, so either one verifies the other.
The driller’s 32nds shortcut, and mixed nozzle sizes
Because a nozzle diameter in 32nds is D = N/32 inches, the circle area πD²/4 becomes πN²/(4 × 32²) = N²/1303.8 square inches. Summed over every nozzle, that gives the shortcut the whole drilling industry uses:
Check: (10² + 10² + 10²) ÷ 1303.8 = 300 ÷ 1303.8 = 0.2301 in², matching the tool exactly.
The shortcut is also how you handle the case the tool cannot: mixed nozzle sizes. A bit with three 10/32-in. nozzles and two 12/32-in. nozzles gives (100 + 100 + 100 + 144 + 144) ÷ 1303.8 = 588 ÷ 1303.8 = 0.4510 in². That limitation is now closed: choose Drilling Nozzles (32nds) in the shape dropdown, enter 10, 10, 10, 12, 12, and the tool sums them directly to 0.4510 in² at 0% blockage, matching the shortcut exactly. The Multiple mode still totals identical openings; the drilling mode is the one that mixes sizes.
What the blockage factor models
Real openings are rarely perfectly clean. A ventilation grille, a filter screen, scale buildup inside a pipe, or a partially closed damper all remove part of the geometric area from the flow. The blockage factor is that lost share as a percentage.
A 12 × 8 in. rectangular duct is 96.0000 in² gross. With a 15% blockage factor (a dirty filter, say), the blocked area is 14.4000 in², the net flow area is 81.6000 in², and the efficiency reads 85.00%. Note the efficiency is simply 100 minus the blockage; the factor is doing one job, not two.
Blockage is an estimate you supply, not something the calculator measures. For design work, grille manufacturers publish free-area ratios for their products, which is the honest source for the percentage rather than a guess.
Where drillers, HVAC designers and hydraulics engineers use TFA
The same number answers different questions in different trades:
- Drilling (bit hydraulics): TFA sets the jet velocity through the bit nozzles for a given mud pump rate, which drives hole cleaning and rate of penetration. Smaller TFA at the same flow means faster jets and higher pressure drop at the bit. The AAPG’s wellsite math references the equivalent jet-nozzle formula, 0.000767 × ΣJ².
- HVAC (duct sizing): the cross-section of a duct is the A in Q = A × V. A 10-inch round duct at 600 fpm carries about 327 CFM because its area is 0.545 ft². This calculator produces the area; the velocity comes from your system design. The duct volume calculator totals the volume of a duct run, and the duct bend area calculator handles elbows and fittings.
- Hydraulics and process piping: orifice plates, valve trim and perforated plates all get their flow capacity from their open area, with discharge coefficients applied afterward. The tool’s area is the starting point, not the flow rate; the hose flow rate calculator and the flow rate pressure calculator carry the area into flow-rate math.
- Combustion air openings: fuel-gas codes size openings by free area per BTU of appliance input (for example, 1 in² per 4,000 BTU/hr for direct outdoor communication), which is a blockage-factor problem in disguise once a grille covers the hole.
The honest scope statement: this page’s tool computes flow area from geometry. It does not convert units, size a duct from a target CFM, or compute flow rates and pressure drops. The use cases above show where the area number goes next, so you know which companion calculation to reach for; several are linked below.
What competing calculators miss
TFA tools split into two tribes that barely talk to each other:
- Drilling TFA pages (calculatorultra-style): the 32nds formula done right, with the N²/1303.8 shortcut and worked nozzle examples, but the tool itself usually assumes identical nozzles and offers no blockage concept and no other shapes.
- Drilling explainers (savvycalculator-style, manufacturer TFA charts): correct worked examples (3 × 10/32 in. → 0.000148 m²) and handy printed charts, but no interactive blockage adjustment and no duct shapes.
- Industry references (AAPG wellsite math): the authoritative jet-nozzle area formula (0.000767 × ΣJ²), written for rig math, not as a calculator.
- Duct area tools (calculife-style, HVAC duct calculators): round and rectangular cross-sections with unit conversion and even surface area for material takeoffs, but nothing for multiple openings, no ellipse or triangle, and no blockage factor.
- CFM-first HVAC tools (numbrwiz-style, ductulator guides): they start from airflow and velocity and solve for size, which is the reverse direction. Useful for design, but they never report the plain geometric area this page centers on.
- The gap this page fills: six shapes in one tool including the multiple-openings mode that doubles as the identical-nozzle case, a blockage factor no rival offers, the 32nds shortcut taught and cross-checked against the tool, plus a drilling-nozzle mode that sums mixed sizes directly, and an explicit statement of the tool’s unitless, area-only scope instead of implied units.
Frequently asked questions
The open area a fluid actually has to pass through. For one duct or pipe it is the cross-sectional area; for a set of identical openings, such as drill-bit nozzles, it is the number of openings times the area of one. It is always a positive area, never a rate.
None of its own. The calculator is unitless: enter inches and read square inches, enter centimeters and read square centimeters, enter millimeters and read square millimeters. Keep every input in the same unit, and do any unit conversion yourself before entering numbers.
A nozzle size spoken as “10” means 10/32 of an inch in diameter. The rig-floor shortcut is TFA = (N1² + N2² + …) ÷ 1303.8 square inches, where each N is a nozzle size in 32nds. Three 10/32-in. nozzles give (100 + 100 + 100) ÷ 1303.8 = 0.2301 in², exactly what this calculator’s Multiple mode produces, and the Drilling Nozzles mode produces the same figure from the list 10, 10, 10.
Use the Drilling Nozzles (32nds) mode and enter 10, 10, 10, 12, 12. The tool sums the squares and divides by 1303.8, giving 0.4510 in² at 0% blockage. The older hand-sum of rounded per-nozzle areas (0.2301 + 0.2208 = 0.4509 in²) differs only by rounding; the mode uses the exact formula.
It subtracts the share of the opening that fluid cannot use, such as a grille, filter screen or scale buildup. Net area = gross × (1 − blockage ÷ 100), and flow efficiency = 100 − blockage. A 15% blockage on a 96 in² duct leaves 81.6 in² net at 85.00% efficiency.
Because most people measure the full span across an opening. The tool halves each axis internally (area = π × (a ÷ 2) × (b ÷ 2)), so entering semi-axes by mistake would quarter your answer. Measure the longest and shortest full spans.
Yes, by hand. Run each shape separately, write down each gross area, and add them. The Multiple mode only totals identical openings, so it cannot mix a circle with a rectangle in one run.
Yes. It runs entirely in your browser, needs no account, and stores nothing. Copy the four results with “Copy my results” or send them to another app with “Share results”.
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References
- AAPG Wiki. Wellsite Math: Bit Hydraulics and Jet Nozzle Area (jet nozzle area = 0.000767 × ΣJ², with the three-13/32-in. worked example = 0.3889 in²). Accessed October 24, 2026.
- Best Diamond Bit. Total Flow Area (TFA) Chart (TFA = ΣN² ÷ 1303.8 for nozzle sizes in 32nds; 3 × 10/32 + 2 × 12/32 worked example = 0.451 in²). Accessed October 24, 2026.
- H2X Engineering. How to Calculate Duct Size for HVAC Systems (A = Q ÷ V: airflow divided by design velocity gives required cross-sectional area; worked main-and-branch example). Accessed October 24, 2026.
- ArchSupply. Duct Sizing Calculator (documents A = Q ÷ V and d = √(4A ÷ π) with worked CFM examples). Accessed October 24, 2026.
- CalcEngineer. Duct Velocity Calculator (documents round and rectangular duct area formulas and the velocity = airflow ÷ area relationship). Accessed October 24, 2026.