Calculate an angle from rise and run for construction or boat building.
Common transom deadrise
Standard 45-degree angle
A slight bevel for a panel edge
Vertical measurement
Horizontal measurement
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Download NowAlmost every cutting, setting-out and rigging job in boatbuilding reduces to a right triangle, and the angle calculator is the tool that turns a rise and a run into the number your saw, your protractor or your cleat actually needs. Given the two legs of a triangle it returns the angle and its useful relatives.
The core is the arctangent of rise over run, expressed in degrees, and alongside it come the same angle in radians, the percentage slope that trades and builders quote, and the complementary and supplementary angles that appear when a joint or line meets another at a corner.
Enter a vertical rise and a horizontal run, and the calculator returns the angle, its radian value, the slope percentage and the related angles, so a single measurement feeds every downstream cut or layout mark.
Angle = arctan(Rise ÷ Run); Slope % = (Rise ÷ Run) × 100; Complement = 90° − Angle; Supplement = 180° − Angle| Rise : Run | Angle | Slope % | Where It Shows Up |
|---|---|---|---|
| 1 : 12 | ≈ 4.8° | 8.3% | Deck camber, gentle sheer |
| 1 : 4 | ≈ 14.0° | 25% | Ramps, light deadrise |
| 1 : 3 | ≈ 18.4° | 33.3% | Typical ladder, spreaders |
| 1 : 1 | 45° | 100% | Bisected corner, chine |
Common rise-over-run ratios and their angles.
Formula verified against standard naval-architecture references · Updated October 2026
Divide the rise by the run and take the arctangent of that ratio to get the angle in degrees from the horizontal. A 12 inch rise over a 36 inch run is arctan(0.333), about 18.4 degrees. The calculator returns that angle plus the same value in radians, the slope percentage and the complementary and supplementary angles, so one measurement serves every layout and cut you need.
It is what you add to the given angle to reach 90 degrees, and it appears constantly because a right-angle joint splits into two complementary halves. If a saw sits off the vertical rather than the horizontal, its setting is the complement of the incline you measured. The calculator reports it so you can pick whichever angle your tool's scale is referencing.
Divide rise by run and multiply by 100. A 12 inch rise over 36 inches is 0.333 times 100, a 33.3 percent slope. Trades and drainage work quote gradient as a percent, so having both the degree angle and the percentage from the same measurement lets one set of numbers satisfy the builder and the saw alike.
Degrees for cutting and setting out, radians when feeding the angle into further trigonometry or a machine. Most hand tools and bevel gauges read degrees, so that is the number to mark; radians appear in programming, formulas and some CNC, and the calculator gives both from the same rise and run so you never have to convert by hand.
Usually because the two mating pieces reference perpendicular faces, so what looks like a mismatch is really a complement relationship, or because rise and run were measured off a line that was not truly square. Verify the reference face, use the complement when needed, and re-measure the legs plumb and level, and the geometry will close.
It is what you add to reach 180 degrees, and it shows up when a line turns through a straight run, such as an obtuse chine or a frame meeting a flat panel. The supplement tells you the angle on the far side of a straight edge, useful when laying out bends, mitres along a run or any joint measured from a straight baseline rather than a right angle.