Formula Used
Diameter taper mode:
Side rise per foot = Taper per foot ÷ 2
Angle in degrees = atan(Side rise per foot ÷ 12) × 180 ÷ π
Included angle = 2 × Side angle
Single-side rise mode:
Angle in degrees = atan(Taper per foot ÷ 12) × 180 ÷ π
Extra outputs:
Percent grade = Side rise per foot ÷ 12 × 100
Ratio = 1 : 12 ÷ Side rise per foot
Total change = Taper per foot × Reference length
How to Use This Calculator
Enter the taper value shown on your drawing or measurement note.
Select the input unit. Choose inches, millimeters, or centimeters per foot.
Choose diameter taper for round workpieces and conical parts.
Choose single-side rise for ramps, wedges, and layout slopes.
Enter a reference length when you need total change.
Select decimal precision. Press Calculate to view the result.
Use CSV or PDF download options for records.
Example Data Table
| Taper |
Mode |
Side Rise |
Angle |
Included Angle |
Ratio |
| 0.500 in/ft |
Diameter taper |
0.250 in/ft |
1.193489° |
2.386978° |
1:48.000000 |
| 1.000 in/ft |
Diameter taper |
0.500 in/ft |
2.385944° |
4.771888° |
1:24.000000 |
| 0.500 in/ft |
Single-side rise |
0.500 in/ft |
2.385944° |
4.771888° |
1:24.000000 |
| 25.400 mm/ft |
Diameter taper |
0.500 in/ft |
2.385944° |
4.771888° |
1:24.000000 |
Practical Taper Conversion
Taper values are common in shop drawings. A shaft, cone, mandrel, wedge, or tool holder may not be written in degrees. Many plans use taper per foot instead. This calculator changes that value into useful angular data. It also shows percent grade and a ratio. These extra outputs help checking, setup, and documentation.
What The Measurement Means
Taper per foot describes change over twelve inches of length. In machine work, it often means total diameter change. A one inch taper per foot means the large diameter changes one inch over twelve inches. The side of the cone only moves half that amount. That half movement gives the working side angle. Some layout jobs use single side rise instead. The mode field lets you choose either method.
Why Degrees Matter
Degrees are easier to set on many tools. A compound slide, saw guide, drafting tool, or digital angle gauge may need an angle. The calculated degree value gives a direct setup target. The included angle helps when a full cone angle is required. Radian output supports technical notes and further calculations.
Accuracy And Precision
Small tapers need careful rounding. A tiny change in taper can create visible error over a long length. The precision option controls shown decimals. Use more decimals for inspection work. Use fewer decimals for quick field layout. Always match the result to your measuring method. Keep original dimensions nearby, so reviewers can trace every final value easily later again.
Using Results In Practice
Start by confirming what the drawing means. Choose diameter taper for round parts and conical fits. Choose single side rise for ramps, wedges, or slope layout. Enter the taper value and its unit. Submit the form. Read the side angle first. Then check the included angle, grade, and ratio.
The ratio shows how many units of run create one unit of side rise. A large ratio means a shallow taper. A small ratio means a steep taper. Percent grade is useful for construction style comparisons. CSV export stores numeric results. The PDF button creates a simple report for records.
Good taper conversion avoids guesswork. It keeps angles, grades, and ratios connected. It also makes repeated shop calculations faster and more consistent.
FAQs
What is taper per foot?
Taper per foot is the amount of size change over twelve inches of length. In machining, it usually means diameter change. In layout work, it may mean single-side rise.
How do I convert taper per foot to degrees?
Convert the taper to inches per foot. Divide by two for diameter taper. Then use atan(side rise divided by twelve). Convert radians to degrees by multiplying by 180 divided by π.
What is included angle?
Included angle is the full angle between both sides of a tapered shape. For a symmetric cone, it equals two times the side angle from the centerline.
When should I use diameter taper mode?
Use diameter taper mode for shafts, pins, cones, mandrels, and machine tapers. It treats the entered value as total diameter change over one foot.
When should I use single-side rise mode?
Use single-side rise mode for ramps, wedges, slopes, and layout problems. It treats the entered value as direct rise over twelve inches of run.
What does the ratio mean?
The ratio shows run compared with one unit of side rise. A result of 1:24 means one unit of rise occurs over twenty-four units of run.
Why is percent grade included?
Percent grade helps compare taper with slope style measurements. It is side rise divided by run, then multiplied by one hundred.
Can I download the results?
Yes. Use the CSV button for spreadsheet records. Use the PDF button after calculation to save a simple report with the main outputs.