The Arc Length Calculator is a free tool that helps you calculate arc length using the formula Arc = 2 pi r x (angle/360); Sector area = pi r^2 x (angle/360). Enter your values above and press Calculate to get arc length, sector area instantly, with a full step-by-step breakdown.
What is the Arc Length Calculator?
The arc length calculator is a free online tool that helps you calculate arc length quickly and accurately. It applies the standard formula Arc = 2 pi r x (angle/360); Sector area = pi r^2 x (angle/360) to the values you enter and, when you press Calculate, displays the result together with a clear, step-by-step explanation of how the answer was reached.
Also known as: arc length formula.
How to use the Arc Length Calculator
- Enter the radius.
- Enter the central angle in degrees.
- See arc length and sector area.
Formula used
The arc length calculator is based on this formula:
Arc = 2 pi r x (angle/360); Sector area = pi r^2 x (angle/360)Each term in the formula corresponds to one of the inputs explained below. The calculator performs the arithmetic for you and shows every step so you can check the working by hand if you wish.
Worked example
Suppose you enter r 5, angle 60. The calculator works as follows:
| Inputs | r 5, angle 60 |
|---|---|
| Working | 2 pi 5 x 60/360 |
| Result | Arc about 5.24 |
Step-by-step calculation
- Apply the formula:
Arc = 2 pi r x (angle/360); Sector area = pi r^2 x (angle/360) - Substitute your values: 2 pi 5 x 60/360
- Read the result: Arc about 5.24
Inputs explained
- Radius (units) — the radius used in the calculation.
- Central angle (degrees) — the central angle used in the calculation.
Understanding your result
- Arc length — the calculated arc length in units.
- Sector area — the calculated sector area in sq units.
Benefits and practical uses
The arc length calculator saves time and removes the risk of manual errors when you need to calculate arc length. It is useful for students, professionals and anyone who wants a fast, dependable answer. Results update the moment you press Calculate, work on any device, and can be copied or shared in a single click — and because the maths runs in your browser, your figures stay completely private.
Tips for an accurate result
- Keep all related inputs in the same units.
- Use the worked example above to confirm you are entering values in the right places.
- Review the assumptions below so the result fits your situation.
- Press Reset to clear everything and try a different scenario.
Common mistakes to avoid
- Entering values in the wrong unit (mismatched units give wrong answers).
- Leaving a required field empty — the calculator will ask you to fill it in.
- Rounding inputs too early, which can slightly change the result.
Assumptions and limitations
- Angle in degrees.
Frequently asked questions
What is an arc?
A portion of a circle's circumference between two points.
How do I use the Arc Length Calculator?
Enter your values in the fields, then press the Calculate button to see the result. Use Reset to clear the form and start again. Nothing is calculated until you click Calculate.
What formula does the Arc Length Calculator use?
It uses the standard formula: Arc = 2 pi r x (angle/360); Sector area = pi r^2 x (angle/360). The full step-by-step working is shown with every result so you can verify it.
What information do I need to use the arc length calculator?
You need: radius, central angle. Sensible example values are pre-filled so you can see how it works.
Is the Arc Length Calculator free to use?
Yes. Every DigiToolkit calculator is completely free, with no sign-up, no login and no usage limits.
Does the Arc Length Calculator work on mobile phones?
Yes. The calculator is mobile-first and works on phones, tablets and computers in any modern browser.
Do I need to install an app?
No. The arc length calculator runs directly in your web browser — there is nothing to download or install.
Is my data private when I use this calculator?
Yes. All calculations run inside your browser. The numbers you enter are never uploaded to a server or shared with anyone.
How accurate is the Arc Length Calculator?
It uses the generally accepted formula for arc length and computes to several decimal places. Results are accurate for the assumptions listed on this page.
Can I copy or share my result?
Yes. After calculating, use the Copy button to copy the result, or Share to copy the page link.
Why is nothing showing until I press Calculate?
By design, the calculator only computes when you press Calculate, so you can finish entering all your values first. Press Reset any time to clear everything.
What units does the Arc Length Calculator use?
It works with degrees, units. Keep your inputs in consistent units for an accurate result.