Calculate duct bend area, width, height, bend radius, bend angle, or quantity from the other inputs with unit conversions in inches, feet, cm, or meters.
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Duct Bend Area Formula
The duct bend area calculator uses the bend radius, duct width, bend angle, and quantity to calculate the total duct bend area. Length inputs are converted to inches internally, and the area is converted back to the area unit you select.
DBA = 2*(R + W/2)*pi*(theta/360)*Q
- DBA = duct bend area
- W = duct width
- H = duct height
- R = bend radius
- theta = bend angle in degrees
- Q = quantity of bends
- pi = 3.14159265
When you leave one value blank, the calculator rearranges the formula to solve for that missing value.
W = DBA/(2*(R + H/2)*pi*(theta/360)*Q)
H = DBA/(2*(R + W/2)*pi*(theta/360)*Q)
R = DBA/(2*pi*(theta/360)*Q) - W/2
theta = (DBA/(2*(R + W/2)*pi*Q))*360
Q = DBA/(2*(R + W/2)*pi*(theta/360))
To calculate duct bend area, enter width, height, bend radius, bend angle, and quantity, then leave the duct bend area field blank. To solve for another value, enter the duct bend area and leave only that value blank.
Common Bend Angle Multipliers
The bend angle is used as a fraction of a full 360 degree circle.
| Bend Angle | Multiplier theta/360 | Typical Description |
|---|---|---|
| 30° | 0.0833 | Small offset bend |
| 45° | 0.1250 | Common transition bend |
| 60° | 0.1667 | Moderate bend |
| 90° | 0.2500 | Quarter-turn elbow |
| 180° | 0.5000 | Half-circle return bend |
Length and Area Unit Conversions
The calculator converts all length inputs to inches before applying the formula.
| Unit | Conversion Used | Type |
|---|---|---|
| 1 ft | 12 in | Length |
| 1 cm | 0.393701 in | Length |
| 1 m | 39.3701 in | Length |
| 1 sq ft | 144 sq in | Area |
| 1 sq cm | 0.1550 sq in | Area |
| 1 sq m | 1550 sq in | Area |
Duct Bend Area Examples
Example 1: Calculate duct bend area
Given:
- Width = 24 in
- Height = 12 in
- Bend radius = 18 in
- Bend angle = 90°
- Quantity = 1
DBA = 2*(18 + 24/2)*pi*(90/360)*1
DBA = 47.1239 sq in
The duct bend area is 47.1239 square inches.
Example 2: Calculate bend angle
Given:
- Duct bend area = 94.2478 sq in
- Width = 24 in
- Height = 12 in
- Bend radius = 18 in
- Quantity = 2
theta = (94.2478/(2*(18 + 24/2)*pi*2))*360
theta = 90.00 degrees
The bend angle is 90.00 degrees.
Duct Bend Area FAQ
Why do I need to leave exactly one field blank?
The calculator solves for one unknown value at a time. If more than one value is blank, there is not enough information to solve the formula. If no value is blank, there is no missing value to calculate.
What does quantity mean in the duct bend area formula?
Quantity is the number of identical duct bends. If one bend has an area of 47.1239 sq in and the quantity is 3, the total duct bend area is three times that amount.
Can I mix inches, feet, centimeters, and meters?
Yes. You can select different length units for width, height, and bend radius. The calculator converts those inputs to inches before calculating, then converts the final area to the selected area unit.
