Practice question • 61dtZ-K5pKf-Kw1qt-4vtbm-VuWV6

Radius vs. Diameter: the “twice” relationship (made easy)

Circles have one superpower: radius and diameter are always linked by 2. Once you remember that, you can switch between them quickly—without getting mixed up.

Meet the parts (with a tiny visual)

Radius ( $r$ ): center → edge
Diameter ( $d$ ): edge → edge, passing through the center

Here’s the idea in simple ASCII:

edge      center      edge
  *---------o---------*
        r       r

<----------- d ----------- >

So the diameter is two radii back-to-back.

The only two formulas you need

$d = 2r$
$r = \frac{d}{2}$

That’s it. Everything else is just plugging in numbers and keeping units.

The Two-Step Method (your circle translator)

Step 1: Identify what you’re given

Ask: “Do I have $r$ (radius) or $d$ (diameter)?”

Step 2: Choose the correct conversion + keep units

If you have $r$ and want $d$ : multiply by 2
$d = 2r$
If you have $d$ and want $r$ : divide by 2
$r = \frac{d}{2}$

Units stay the same (cm stays cm, inches stays inches, etc.).

Worked Example 1 (cm, symbolic → numeric)

Given: $r = 7\text{ cm}$

Step 1: Given radius.

Step 2: Convert to diameter using $d = 2r$ :

$d = 2(7\text{ cm}) = 14\text{ cm}$

Result: $d = 14\text{ cm}$

Worked Example 2 (mm, diameter → radius)

Given: $d = 48\text{ mm}$

Step 1: Given diameter.

Step 2: Convert to radius using $r = \frac{d}{2}$ :

$r = \frac{48\text{ mm}}{2} = 24\text{ mm}$

Result: $r = 24\text{ mm}$

Worked Example 3 (inches, fractional/decimal)

Let’s do one that feels a bit more “real life.”

Given: $r = 2.5\text{ in}$

Step 1: Given radius.

Step 2: Convert to diameter using $d = 2r$ :

$d = 2(2.5\text{ in}) = 5\text{ in}$

Result: $d = 5\text{ in}$

(And if it were a fraction like $r = 2\tfrac{1}{2}\text{ in}$ , it’s the same value as 2.5 in—still doubles to 5 in.)

Important warning: don’t round too early

When your radius or diameter comes from a measurement or a calculation, you might see decimals that don’t end nicely. The trap is rounding too soon.

Why it matters

If you round early, then multiply or divide, the final answer can drift.

Example of the idea:

Suppose $d = 9.7\text{ cm}$
Exact radius is $r = \frac{9.7}{2} = 4.85\text{ cm}$

If you rounded early to $4.9\text{ cm}$ and later used it in more steps, your final result could be off.

Rule of thumb:

Keep exact values (or several decimal places) during the work
Round only at the very end

Quick takeaway (you’ve got this)

Diameter is twice the radius: $d = 2r$
Radius is half the diameter: $r = \frac{d}{2}$
Use the Two-Step Method: what’s given → pick multiply/divide by 2 → keep units
Save rounding for the finish line

Circles are secretly simple—you just have to remember the number 2 runs the show.

Learn faster with bite‑sized practice that actually sticks.