Online Tool Store
Angle Converter
Convert an angle between degrees, radians, gradians, turns, arcminutes and arcseconds all at once, with its sine, cosine and tangent. Runs in your browser.
🔒 This tool runs entirely in your browser. Your files are never uploaded to a server.
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Example shown — enter your own value.
All units
| Unit | Value | Copy |
|---|
Trigonometric values
- sin
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- cos
- —
- tan
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How it works
- Enter an angle and say what unit it is in.
- Pick a target unit for the headline, or read every unit from the table below.
- Optionally wrap the angle into a single turn, and set the precision you need.
- Check the sine, cosine, and tangent underneath if you are heading into trigonometry.
One base unit, seven views of the same angle
Every unit is defined against degrees, so a conversion is one multiply and one divide — and no two units can ever disagree with each other:
degrees = value × factor(from)
result = degrees ÷ factor(to)
The whole system hangs off one identity, which is worth committing to memory:
1 turn = 360° = 2π rad ≈ 6.283185 rad = 400 gon
So a right angle is 90°, exactly π/2 ≈ 1.570796 radians, 100 gradians, a quarter turn, 5400 arcminutes, or 324,000 arcseconds — all the same angle. One radian works out at about 57.295780°, which is why radians rarely give round numbers in degrees and vice versa.
Where tan genuinely breaks
Tangent is sine divided by cosine, and at 90° the cosine is zero — so the tangent does not exist there. Computers hide this badly:
cos(90°) in floating point = 6.123 × 10⁻¹⁷ // not quite zero
tan(90°) therefore returns ≈ 1.633 × 10¹⁶ // a meaningless huge number
That enormous figure is an artefact of π not being exactly representable in binary, not a real value. This tool detects the 90° + 180°k cases and says "undefined", which is the mathematically honest answer.
FAQ
What actually is a radian?
The angle you get when the arc you have swept out is exactly as long as the radius. That definition is why radians turn up throughout maths and physics: it makes arc length simply radius × angle, with no conversion factor floating around. A full circle is 2π radians because the circumference is 2π radii.
Why do gradians exist?
They are the metric attempt at angle. A right angle is 100 gradians rather than 90 degrees, so a full turn is 400 — which makes percentage-style slope arithmetic tidy. They never displaced degrees generally, but they survive in surveying and on many calculators as the "gon" or "grad" mode.
Why is tan sometimes shown as undefined?
Because tan is sine over cosine, and cosine is exactly zero at 90° and every 180° after it — so there is nothing to divide by. A calculator that returns an enormous number there is really telling you about floating-point rounding, not about the tangent, so this says "undefined" instead.
What does "wrap into one full turn" do?
It reduces the angle to its equivalent between 0° and 360°, so 450° becomes 90° and −90° becomes 270°. Handy when an accumulated rotation has run past a full circle and you want the direction it actually faces.
What are milliradians for?
Small-angle work — rifle scopes, surveying, and optics. One milliradian is a thousandth of a radian, which conveniently subtends about 1 unit at 1000 units of distance, so it makes range estimation arithmetic simple.
Why are arcminutes and arcseconds included?
They are how astronomy and navigation subdivide a degree: 60 arcminutes to a degree and 60 arcseconds to an arcminute, the same sexagesimal system as hours and minutes. Coordinates and telescope resolutions are still quoted this way.
How we compare
| Feature | Online Tool Store | Search engine answer box | Scientific calculator |
|---|---|---|---|
| Every unit at once, not one pair | ✓ | One conversion at a time | One mode at a time |
| Says "undefined" for tan at 90° | ✓ | Often a huge number | Usually an error code |
| Arcminutes, arcseconds, milliradians | ✓ | Hit and miss | Degrees/radians/grads only |
| Nothing typed leaves the page, no ads | ✓ | ✗ | ✓ |
| Inverse trig, and full expression evaluation | ✗ | ✓ | ✓ |
| Degrees-minutes-seconds as one combined input | ✗ | Sometimes | ✓ |
Useful when a formula wants radians and your drawing is in degrees, when a calculator is stuck in grad mode, or when you need the same angle in several notations at once. It converts a single value — combined degrees-minutes-seconds input and inverse trig are calculator territory.