Radians To Seconds Converter

radian to second – How to convert rad to ″

Radians and arcseconds might sit on opposite ends of the angle scale—one used in pure math and physics, the other in high-precision measurements like astronomy, geodesy, and satellite positioning. Still, converting between them is crucial when you're working across systems that handle angles in vastly different units.

Let’s look at what each unit means, how they compare, and how to convert radians to arcseconds with just one calculation.

What is a radian (rad)?

A radian is the SI unit for measuring angles. It’s defined based on the geometry of the circle—one radian is the angle formed when the arc length equals the radius:

• 1 full circle = 2π radians

• 1 rad ≈ 57.2958 degrees

Radians are most commonly used in mathematics, physics, rotational motion, and engineering formulas—especially those involving trigonometric functions.

What is a second (″) of arc?

A second of arc, or arcsecond, is a very small unit of angular measurement:

• 1 degree = 60 arcminutes (′)

• 1 arcminute = 60 arcseconds (″)

• So, 1 degree = 3,600 arcseconds

This unit is essential when extreme accuracy is required, such as:

• Astronomical positioning

• GPS signal precision

• Telescope alignment

• High-end land surveying

When radians describe entire rotations in math, seconds of arc describe microscopic angular differences in the sky or on Earth.

How to convert radian to second

Since:

• 1 radian ≈ 57.2958 degrees

• 1 degree = 3,600 arcseconds

We can combine these steps into a single formula.

Formula

second = radian × 206,264.806

This is the number of arcseconds in one radian, derived by:

second = radian × (180 / π) × 3,600
second ≈ radian × 206,264.806

Example: Convert 0.002 radians to arcseconds

second = 0.002 × 206,264.806
second ≈ 412.53

So, 0.002 radians equals approximately 412.53 arcseconds.

Use the Angle Converter for quick and accurate conversions, or explore our full range of Conversion tools for other angle units.

Did you know?

• The Hubble Space Telescope has a resolution of about 0.05 arcseconds—enough to distinguish a beach ball 500 km away.

• GPS satellites rely on angular data down to the arcsecond to pinpoint your location within a few centimeters.

• The Earth’s rotation shifts some stars' positions by fractions of arcseconds each year—a key part of astrometry.

• Military-grade optics and laser systems often operate at arcsecond-level precision to ensure targeting accuracy.

• In telescope mounts, one arcsecond misalignment can throw off deep-sky observations by several arcminutes.

From equations to the edge of the galaxy

In a classroom, radians are a go-to unit for solving trigonometric problems. But in the real world—when tracking a satellite or locating a distant star—we need measurements that go far smaller than a radian. That’s why arcseconds exist.

Astronomers, engineers, and GPS developers often convert radians to seconds so they can fine-tune systems that deal with objects thousands (or millions) of kilometers away. And because precision matters, even a fraction of a radian can become thousands of arcseconds.

Final conversion for high-precision work

If your work involves detailed navigation, astronomical data, or geodetic modeling, converting radians to arcseconds isn’t optional—it’s essential.

Keep the formula in mind:

second = radian × 206,264.806

And when you want results fast, the Angle Converter is your best tool. For other scientific or engineering unit conversions, browse the full selection of Conversion tools anytime.