Convert angles between degrees, radians, gradians, turns, arcminutes, and arcseconds. See trigonometric values, DMS notation, quadrant, and a full common-angles reference table.
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 get wrong without the right tool.
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 can be 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 an indispensable quick-reference for homework, exams, or professional work.
This angle conversion calculator reduces manual rework when you need quick checks for assignments, exam prep, and design calculations. You can enter Angle Value, Source Unit, Decimal Places and immediately see dependent measurements, validity checks, and geometry relationships in one place. That makes it easier to catch input mistakes early and confirm your final answer before moving to the next step.
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 × 60
Result: For val=0, unit=degrees, the tool returns the solved angle conversion outputs shown in the result cards.
This example uses a realistic input set from the calculator workflow. After entry, the calculator applies the built-in angle conversion formulas and reports derived values, checks, and classifications automatically.
This page is tailored to angle conversion, with outputs tied directly to the form fields (Angle Value, Source Unit, Decimal Places). Instead of a one-line formula dump, it consolidates validation, derived metrics, and interpretation so you can solve and verify in one pass.
Use this tool for homework checks, worksheet generation, tutoring walkthroughs, and quick engineering geometry estimates. Presets and visual output blocks make it easier to compare scenarios and understand how each input affects the final result.
Keep units consistent, match each value to the correct field, and watch validity indicators before using the final numbers. If your case looks off, change one input at a time and use the output details to identify the mismatch quickly.
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.