# Standard Form to General Form of a Circle Calculator

Are you looking for a quick way to convert the circle equation from standard form to general form? Then our **standard form to general form of a circle calculator** is a perfect match for you.

Please read this short article to learn more about:

- How to use our standard form to the general form of a circle calculator?; and
- How to convert the circle equation from
**standard form to general form**?

## How to use our standard form to general form of a circle calculator?

To use our calculator, you can use the following guide:

- Make sure your circle equation is in standard form: $(x-h)^2 +(y-k)^2=\text{C}$;
- Insert the parameters:
**h, k, and C**present in standard form into the respective fields; and - Right away, you will get
**the circle equation in a general form**.

Nice, you are an expert in using our calculator now ;).

## How to convert the circle equation in standard form to general form ?

To convert the circle equation from the standard to general form, you can use the following steps:

**Extract the radius and center information from the standard form**. You can see below from the standard form we can observe the variables`h`

, and`k`

, which correspond to the center, and r corresponds to the radius.

- General form of the circle equation is given as:

- Now, use the following formula to compute the coefficients of the general form:

- Finally, substitute the values obtained to get the circle equation in a general form.

Excellent, you have learned how to convert circle equation from standard form to general form.

## More calculators to assist you

Check out our circle-related calculators created to assist you in solving circle-related problems. Whenever you need them, they will be available here:

- Equation of a circle calculator;
- Center of a circle calculator;
- General form of the equation of a circle calculator;
- Standard equation of a circle calculator;
- Equation of a circle with diameter endpoints calculator;
- General to standard form of a circle calculator;

## FAQ

### What is the general form of a circle equation with diameter endpoints (4,8), (6,6)?

The general form is given as `x²+y²-10x-14y+72=0`

. To find the general form, start with the general form `x²+y²+Dx+Ey+F=0`

, and let's find the coefficients using the following steps:

- Find the center
`(h,k)`

and distance between the diameter endpoints using the midpoint and distance formulas, respectively. - Divide the distance found in step
**1**by`2`

to obtain the radius`r=1.4142`

. - Calculate the coefficients of the general form using the following equation:

`D=-2×h=-10`

;

`E=-2×k=-14`

; and

`F=h²+k²-r²=72`

. - substitute the coefficients to obtain the circle equation in a general form:

`x²+y²-10x-14y+72=0`

### How do I find the radius from circle equation in general form?

To find the radius from the general form, use the following steps:

- Extract the coefficients from the general form:
`x²+y²+Dx+Ey+F=0`

; - Use the formula of
`F`

which is given as`F=(D/2)²+(E/2)²-r²`

. - Rearrange the formula of
`F`

in terms of radius`r`

:`r=√((D/2)²+(E/2)²-F)`

; and - Solve the equation in
**step 3**to obtain the radius of the circle.

Hooray! Now you know how to find the radius if you are given with circle equation in a general form.