Answer first
What this calculator tells you
Convert between degrees, radians, gradians, arcminutes, arcseconds and turns. Switch a calculator, a program or a survey between the angle units it expects. Formula: Result = value × (from-unit factor ÷ to-unit factor), factors relative to degrees. At the worked-example inputs, the converted value is 3.1416. Holding every other input steady, moving value from 144 to 216 moves the result from 2.5133 to 3.7699.
Transparent method
The formula
Switch a calculator, a program or a survey between the angle units it expects.
Worked example
Example inputs
How to interpret the result
Angles are measured in different units in different fields, and the conversions all hang on one fact: a half turn is 180 degrees and also pi radians. So 180 degrees is 3.1416 radians, and one radian is about 57.2958 degrees. Programming languages and calculus want radians. Maps, blueprints and survey work use degrees, arcminutes and arcseconds, and construction speaks in degrees. Reference values: a full turn is 360 degrees, 2 pi radians or 400 gradians, and a degree is 60 arcminutes or 3,600 arcseconds. A right angle is 90 degrees, about 1.5708 radians.
At the worked-example inputs the converted value is 3.1416. It rises with from and value and falls as to increases.
Conversion factors are exact defined constants; results are limited only by floating-point precision, not by real-world estimation.
Before you rely on it
What to check
Confirm the unit your tool expects before you type a value. A sine function fed degrees when it wants radians returns a plausible but wrong number.
The common error
Where people go wrong with angle converter calculator
Treating arcminutes as hundredths of a degree. There are 60 arcminutes in a degree and 60 arcseconds in an arcminute, not 100.
Sensitivity evidence
How value changes the converted value
Holding every other input at the worked-example value, moving value from 144 to 216 moves the converted value from 2.5133 to 3.7699: a spread of 1.2566, or 40% of the worked-example result.
| Value | Converted value | 1 unit of "from" in "to" units |
|---|---|---|
| 144 | 2.5133 | 0.0175 |
| 162 | 2.8274 | 0.0175 |
| 180worked example | 3.1416 | 0.0175 |
| 198 | 3.4558 | 0.0175 |
| 216 | 3.7699 | 0.0175 |
Every input, tested
Which input moves the converted value most
Of the 3 inputs, from moves the converted value most (1127.8318 across the range tested) and value moves it least (0.6283).
| Input | Tested from | To | Converted value at each end | Swing |
|---|---|---|---|---|
| From | Degrees | Turns | 3.1416 to 1130.9734 | 1127.8318 (36000%) |
| To | Degrees | Turns | 180.0000 to 0.5000 | 179.5000 (20626465%) |
| Value | 162 | 198 | 2.8274 to 3.4558 | 0.6283 (20%) |
Step by step
The worked example, input by input
| Input | Value used | What it means |
|---|---|---|
| Value | 180 | Enter the value used in this calculation. |
| From | Degrees | Unit to convert from. |
| To | Radians | Unit to convert to. |
| Converted value | 3.1416 | |
| 1 unit of "from" in "to" units | 0.0175 | |
Inputs, definitions and assumptions
Value
Enter the value used in this calculation. The prefilled worked-example value is 180.
From
Unit to convert from. The prefilled worked-example value is Degrees.
To
Unit to convert to. The prefilled worked-example value is Radians.
How to use this calculator
- 1Verify the inputs. Gather value, from and to from your own documents; the prefilled values are examples.
- 2Save a baseline. The worked example puts the converted value at 3.1416. Store your own version of it as Scenario A.
- 3Test one change. Start with from, the input with the biggest effect here: switching from changes the converted value: degrees gives 3.1416; radians gives 180.0000; gradians gives 2.8274; arcminutes gives 0.0524; arcseconds gives 0.0009; turns gives 1130.9734.
- 4Check the boundary. Read the interpretation boundary above before acting on the result.
People also ask
Frequently asked questions
How do you calculate angle converter?
Result = value × (from-unit factor ÷ to-unit factor), factors relative to degrees. At the worked-example inputs the converted value is 3.1416.
What does the angle converter result mean?
Switch a calculator, a program or a survey between the angle units it expects. At the worked-example inputs the converted value is 3.1416. It rises with from and value and falls as to increases.
How much does value change the converted value?
Holding every other input at the worked-example value, moving value from 144 to 216 moves the converted value from 2.5133 to 3.7699, a spread of 1.2566.
What are the limits of this angle converter calculator?
Conversion factors are exact defined constants; results are limited only by floating-point precision, not by real-world estimation. The tables on this page test value only from 144 to 216; a value outside that range is not tabulated here.
Which input moves the converted value most in the angle converter calculator?
Ranked by how far each moves the converted value across the range tested: from (1127.8318, 36000%), to (179.5000, 20626465%) and value (0.6283, 20%).
How much does from matter in the angle converter calculator?
The worked example uses Degrees. With the other inputs left at the worked example, switching from changes the converted value: degrees gives 3.1416; radians gives 180.0000; gradians gives 2.8274; arcminutes gives 0.0524; arcseconds gives 0.0009; turns gives 1130.9734.
How much does to matter in the angle converter calculator?
The worked example uses Radians. Holding every other input at its worked-example value, switching to changes the converted value: degrees gives 180.0000; radians gives 3.1416; gradians gives 200.0000; arcminutes gives 10800.0000; arcseconds gives 648000.0000; turns gives 0.5000.
Which inputs change the 1 unit of "from" in "to" units in the angle converter calculator?
At the worked-example inputs it is 0.0175. From takes it from 0.0175 to 6.2832 and to takes it from 1.0000 to 0.0028.
Why is a nautical mile 1,852 meters?
It was defined from one minute of latitude, about a sixtieth of a degree along a meridian, and fixed internationally at exactly 1,852 meters. That link to latitude is why ships and aircraft use it for navigation.
Why does fuel economy conversion give a curve, not a straight line?
Miles per gallon divides distance by fuel, and liters per 100 kilometers divides fuel by distance, so one is the reciprocal of the other. Doubling the mpg halves the liters per 100 kilometers, which is not a straight-line change.
Sources and evidence
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