Degrees Calculator

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Degrees & Angle Converter

Convert Decimal Degrees

Radians: rad

Gradians: grad

DMS Format:

Circular Mils: µ

Degrees, Minutes, Seconds to Decimal

Decimal Degrees: °

function calculateFromDecimal() { var val = parseFloat(document.getElementById('decimalDegreesInput').value); if (isNaN(val)) { alert("Please enter a valid numerical value for degrees."); return; } // Radians = deg * (pi / 180) var radians = val * (Math.PI / 180); // Gradians = deg * (400 / 360) var gradians = val * (10 / 9); // Mils = deg * (6400 / 360) var mils = val * (160 / 9); // DMS conversion var d = Math.floor(Math.abs(val)); var minTotal = (Math.abs(val) – d) * 60; var m = Math.floor(minTotal); var s = ((minTotal – m) * 60).toFixed(2); var sign = val < 0 ? "-" : ""; var dmsString = sign + d + "° " + m + "' " + s + "\""; document.getElementById('resRadians').innerText = radians.toFixed(6); document.getElementById('resGradians').innerText = gradians.toFixed(4); document.getElementById('resDMS').innerText = dmsString; document.getElementById('resMils').innerText = mils.toFixed(2); document.getElementById('decimalResults').style.display = 'block'; } function calculateFromDMS() { var d = parseFloat(document.getElementById('dInput').value) || 0; var m = parseFloat(document.getElementById('mInput').value) || 0; var s = parseFloat(document.getElementById('sInput').value) || 0; // Absolute sign check var isNegative = d < 0; var absD = Math.abs(d); // Formula: D + M/60 + S/3600 var decimal = absD + (m / 60) + (s / 3600); if (isNegative) decimal = -decimal; document.getElementById('resDecimal').innerText = decimal.toFixed(6); document.getElementById('dmsResults').style.display = 'block'; }

Understanding Angular Measurements

A degrees calculator is an essential tool for navigation, cartography, engineering, and physics. While most people are familiar with degrees as a way to measure the rotation of a circle (360 degrees being a full rotation), technical fields often require conversion into more precise or mathematically convenient units like Radians or Gradians.

Degrees vs. Radians vs. Gradians

  • Degrees (°): A unit of measurement that divides a circle into 360 equal parts. This originates from ancient Babylonian mathematics.
  • Radians (rad): The standard unit of angular measure used in mathematics. One radian is the angle subtended at the center of a circle by an arc that is equal in length to the radius. Full circle = 2π radians.
  • Gradians (grad): Also known as gons, this unit divides a right angle into 100 parts, meaning a full circle is 400 gradians. It is commonly used in surveying in some parts of Europe.

What are Degrees, Minutes, and Seconds (DMS)?

Just as an hour is divided into minutes and seconds, a degree is also subdivided for higher precision:

  • 1 Degree = 60 Minutes (')
  • 1 Minute = 60 Seconds (")
  • 1 Degree = 3,600 Seconds

This format is most common in GPS coordinates (Latitude and Longitude) and marine navigation. For example, a coordinate might be written as 45° 30′ 00″, which is exactly 45.5 degrees in decimal format.

Common Conversion Examples

Degrees Radians DMS
90° π/2 (1.5708) 90° 0′ 0″
180° π (3.1416) 180° 0′ 0″
45.25° 0.7898 45° 15′ 0″

Formula for Conversion

To convert from Degrees to Radians manually, use the formula:

Radians = Degrees × (π / 180)

To convert DMS to Decimal Degrees:

Decimal = Degrees + (Minutes / 60) + (Seconds / 3600)

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