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How to Calculate Bow Window Angles

Updated March 23, 2017

In a bow window, three walls or panes set at angles project out of a room. Unlike similar bay windows, a bow window's panes may be curved, but architects describe their angles as though they were straight. Some common angles for bow and bay windows include 90, 130 and 150 degrees. Some windows use other angles as well, and you can calculate any bow window's angles by applying trigonometric ratios to the window's linear measurements.

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  1. Measure the width of the central pane. For instance, this pane may measure 25 inches.

  2. Measure the entire bay's width. For instance, the bay may be 50 inches in width.

  3. Subtract the central pane's width from the whole bay's width. With this example: 50 - 26 = 24 inches.

  4. Divide this answer by 2: 24 ÷ 2 = 12 inches.

  5. Measure the bay's depth. For instance, it may have a depth of 14 inches.

  6. Divide the measurement from Step 4 by the measurement from Step 5: 12 ÷ 14 = 0.857.

  7. Find the inverse tangent of this ratio: tan-1(0.857) = 40.6.

  8. Add this answer to 90: 90 + 40.6 = 130.6, or just over 130. The bow windows are set at this angle.

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Things You'll Need

  • Tape measure
  • Scientific calculator or computer

About the Author

Ryan Menezes is a professional writer and blogger. He has a Bachelor of Science in journalism from Boston University and has written for the American Civil Liberties Union, the marketing firm InSegment and the project management service Assembla. He is also a member of Mensa and the American Parliamentary Debate Association.

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