Unit Circle Calculator — Trig Values, Coordinates & Quadrants
Enter any angle in degrees or radians to find sin, cos, tan, csc, sec, cot, (x, y) coordinates, quadrant, and reference angle on the unit circle. Common angles table included.
Angle Conversion Calculator — Degrees, Radians, Gradians & More
Convert angles between degrees, radians, gradians, turns, arcminutes, and arcseconds. See trigonometric values, DMS notation, quadrant, and a full common-angles reference table.
Angle Conversion Calculator
Degrees (°)⧉
0.000000
Standard degree measure — one full revolution = 360°
Radians (rad)⧉
0.000000
SI angle unit — one full revolution = 2π ≈ 6.2832 rad
Gradians (gon)⧉
0.000000
Used in surveying — one full revolution = 400 gon
Turns⧉
0.000000
Fraction of a full revolution — 1 turn = 360° = 2π rad
Arcminutes (′)⧉
0.000000
1/60 of a degree — used in navigation and astronomy
Arcseconds (″)⧉
0.000000
1/3600 of a degree — used in precision astronomy
DMS Notation⧉
0° 0′ 0.00″
Degrees, minutes, seconds format commonly used on maps
Quadrant⧉
Positive x-axis
Location of the terminal side on the unit circle
Trigonometric Values
sin(θ)⧉
0.000000
Opposite / hypotenuse on the unit circle
cos(θ)⧉
1.000000
Adjacent / hypotenuse on the unit circle
tan(θ)⧉
0.000000
sin(θ) / cos(θ) — undefined when cos = 0
Trig Value Comparison
sin(θ)
0.0000
cos(θ)
1.0000
tan(θ)
0.0000
Common Angles Reference
| Degrees | Radians | Gradians | Turns | sin | cos | tan |
|---|---|---|---|---|---|---|
| 0° | 0.0000 | 0.00 | 0.0000 | 0.0000 | 1.0000 | 0.0000 |
| 30° | 0.5236 | 33.33 | 0.0833 | 0.5000 | 0.8660 | 0.5774 |
| 45° | 0.7854 | 50.00 | 0.1250 | 0.7071 | 0.7071 | 1.0000 |
| 60° | 1.0472 | 66.67 | 0.1667 | 0.8660 | 0.5000 | 1.7321 |
| 90° | 1.5708 | 100.00 | 0.2500 | 1.0000 | 0.0000 | — |
| 120° | 2.0944 | 133.33 | 0.3333 | 0.8660 | -0.5000 | -1.7321 |
| 135° | 2.3562 | 150.00 | 0.3750 | 0.7071 | -0.7071 | -1.0000 |
| 150° | 2.6180 | 166.67 | 0.4167 | 0.5000 | -0.8660 | -0.5774 |
| 180° | 3.1416 | 200.00 | 0.5000 | 0.0000 | -1.0000 | -0.0000 |
| 210° | 3.6652 | 233.33 | 0.5833 | -0.5000 | -0.8660 | 0.5774 |
| 225° | 3.9270 | 250.00 | 0.6250 | -0.7071 | -0.7071 | 1.0000 |
| 240° | 4.1888 | 266.67 | 0.6667 | -0.8660 | -0.5000 | 1.7321 |
| 270° | 4.7124 | 300.00 | 0.7500 | -1.0000 | -0.0000 | — |
| 300° | 5.2360 | 333.33 | 0.8333 | -0.8660 | 0.5000 | -1.7321 |
| 315° | 5.4978 | 350.00 | 0.8750 | -0.7071 | 0.7071 | -1.0000 |
| 330° | 5.7596 | 366.67 | 0.9167 | -0.5000 | 0.8660 | -0.5774 |
Planning notes, formulas, and examples
About the Angle Conversion Calculator — Degrees, Radians, Gradians & More
Angles are fundamental to geometry, physics, engineering, navigation, and everyday life. The same angle can be measured in many different units — degrees, radians, gradians, turns, arcminutes, and arcseconds — and converting between them is a routine task that is easy to mishandle when the units change mid-problem.
Degrees divide a full circle into 360 equal parts and are the most familiar unit in everyday use. Radians, the SI unit of angle, define one full revolution as 2π and are essential in calculus, physics, and programming. Gradians (also called gon or grad) split the circle into 400 parts and are popular in surveying and civil engineering because a right angle is exactly 100 gon. Turns express an angle as a fraction of a full revolution. Arcminutes (1/60 of a degree) and arcseconds (1/3600 of a degree) provide the precision needed in astronomy, navigation, and cartography.
This calculator converts any angle value you enter into all six units simultaneously. That is useful for students learning trigonometry, engineers switching between standards, or navigators interpreting GPS coordinates in DMS (degrees-minutes-seconds) format. It also computes the sine, cosine, and tangent at the given angle, identifies which quadrant the angle lies in, and provides a visual bar chart comparing the trig values. The common-angles reference table at the bottom lists the 16 standard unit-circle angles with their exact values in every unit, making it a practical quick reference for homework, exams, or technical work.
When This Page Helps
Use this page when one angle has to be expressed across multiple unit systems. It keeps the converted units, DMS notation, quadrant, and trig values aligned so you can move between degrees, radians, gradians, turns, and sub-degree units without losing context.
How to Use the Inputs
- Enter an angle value in the input field (any positive or negative number).
- Select the source unit from the dropdown: degrees, radians, gradians, turns, arcminutes, or arcseconds.
- Or click any preset button for a standard angle.
- All six converted values appear in the output cards.
- View the DMS (degrees-minutes-seconds) notation and the quadrant.
- Check the trigonometric values (sin, cos, tan) and the visual comparison bars.
- Scroll down to the common-angles reference table for standard values.
- Adjust decimal places with the precision control (0–12).
Formula used
Radians = Degrees × π / 180
Degrees = Radians × 180 / π
Gradians = Degrees / 0.9
Turns = Degrees / 360
Arcminutes = Degrees × 60
Arcseconds = Degrees × 3600
DMS: d° = d° m′ s″ where m = floor((frac) × 60), s = remainder × 60Example Calculation
Result: 0° = 0 rad = 0 gon = 0 turns
An input of 0 degrees stays at zero in every supported unit system. The trig values then evaluate to sin 0 = 0, cos 0 = 1, and tan 0 = 0.
Tips & Best Practices
- Most programming languages (JavaScript, Python, C) use radians for trig functions — always convert degrees to radians before calling Math.sin().
- A right angle is 90° = π/2 rad = 100 gon = 0.25 turns exactly.
- DMS notation is standard on maps and GPS devices — this calculator converts automatically.
- Use gradians when working with surveying instruments — many theodolites read in gon.
- Arcminutes and arcseconds are used by astronomers to measure star separations and telescope fields of view.
When To Use This Calculator
Convert angles between degrees, radians, gradians, turns, arcminutes, and arcseconds. See trigonometric values, DMS notation, quadrant, and a full common-angles reference table. Use it when you need a repeatable calculation in the math / geometry category and want the setup, result, and supporting values kept together. This is especially helpful when small input changes, unit choices, or rounding decisions can change the final number.
How To Check The Result
Start by confirming that the inputs match the formula shown on the page. Then compare the main output with the worked example and any secondary values shown by the calculator. If the result will be used in another calculation, keep extra precision until the final step and record the assumptions beside the number.
Practical Notes
Treat the result as a calculation aid rather than a substitute for context. For schoolwork, include the formula and substitution steps. For planning, technical, financial, or health-related decisions, verify important numbers against primary records, current rules, or a qualified professional before acting on them.
Sources & Methodology
Last updated:
Frequently Asked Questions
Degrees divide a full circle into 360 parts; radians use 2π for a full revolution. Radians are dimensionless and are the standard unit in mathematics and physics.
Gradians (gon) split the circle into 400 parts. They are popular in surveying and civil engineering because a right angle is exactly 100 gon, making field calculations simpler.
Decimal degrees = d + m/60 + s/3600. For example, 40° 26′ 46″ = 40 + 26/60 + 46/3600 ≈ 40.4461°.
Yes. Negative angles represent clockwise rotation. The calculator processes them correctly and normalizes for quadrant determination.
A turn is one full revolution — 360° or 2π radians. Half a turn is 180°, a quarter turn is 90°. It is the simplest way to express rotation as a fraction.
They provide sub-degree precision for astronomy, navigation, and cartography. One arcminute ≈ 1.85 km on the Earth's surface; one arcsecond ≈ 31 m.
1 arcminute = 60 arcseconds. Divide arcseconds by 60 to get arcminutes, or multiply arcminutes by 60 to get arcseconds.
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