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Circumference to Diameter Calculator

Range: 0 cm – 1,000,000,000 cm

Range: 0 cm – 1,000,000,000 cm

Result

6.3662 cm

Diameter

Circumference
20.0000 cm

This circumference to diameter calculator does the one conversion that the constant pi is defined by, in both directions at once: type a circumference and read the diameter, or type a diameter and read the circumference. Both figures are printed whichever box you filled, so you never have to know which way round you wanted it before you start. The relationship itself is the definition of pi, and it is worth stating plainly because it is the whole page. Pi is the number you get when you divide any circle's circumference by its diameter — always the same number, about 3.14159, for every circle that has ever existed. Written as an equation, circumference equals pi times diameter; solved for the other side, diameter equals circumference divided by pi. That is the entire conversion, and the two boxes are just those two sentences with somewhere to type the number. Only one of the two boxes is meant to be filled. They are the same measurement of the same circle in two different units of description, so filling both is not more accurate, it is a contradiction: a circumference of 20 and a diameter of 6.3662 do describe one circle, but a circumference of 20 and a diameter of 7 do not, and the page has no way to know which of the two you meant. Fill the one you have and leave the other alone. There is a second reason the arithmetic goes through the radius rather than straight from one box to the other, and it shows up as a practical convenience rather than a mathematical one. The page halves or doubles through a radius and rounds once at the end, so the answers are exact round trips: take the diameter the page prints for a circumference of 20, type that diameter back in, and you get 20 — not 19.9999. That property is worth more than it sounds, because it means you can chain this page with any other circle page and the numbers will still line up. Enter the same measurements on the overview page and its diameter, radius and circumference all agree with the two figures here to the last digit. The units work the same way as everywhere else on this site. Either box accepts centimetres, metres, millimetres, inches or feet, and both answers come back in centimetres, because the conversion happens on the way in. A circumference measured in inches comes back as a centimetre figure about two and a half times larger. Nothing here is squared, so the divisor is 2.54 and not the square of it. One thing to expect before you read the results. Both lines appear whichever box you filled, and the first line is always the diameter. Enter a diameter and the first line is simply the number you typed, echoed back, with the circumference you asked for on the second line. That ordering is deliberate rather than an oversight, and it is the price of having both directions on one page without a mode to choose between them.

Common circles: the circumference for a given diameter, and the diameter for a given circumference

Circumference (cm)Diameter (cm)
3.14161
6.28322
9.42483
15.7085
31.415910
62.831920
1.57080.5
00

Eight circles in two columns, and either column can be read as the answer. The table is built from the diameters, which is why those are the round numbers and the circumferences are the ones carrying long decimals: the second column is the measurement people can take, and the first is the one they usually want. The first row is the unit circle, whose circumference is π to four places — the quickest way to remember that a diameter of 1 goes around in a little over 3. The first two rows are the scaling pair: the diameter doubles and the circumference doubles with it, because a circumference is a length and not an area. The fourth row is a diameter of 5, going around in 15.708, and it is the row to look at when your measurement is somewhere near sixteen. The fifth is a diameter of 10, and its circumference of 31.4159 is the figure the circumference page and the ellipse page both print for the same circle — it is the circle the circumference page loads with, a radius of 5. The circumference this page loads with, 20, falls between those two rows, which is why the diameter it prints sits between their diameters. The seventh is a diameter of half a centimetre, the smallest circle in the table, and it is there to show how far down the four decimals still reach: at this size the display is finer than anything a tape could measure, which is worth knowing before reading precision into the last digit. The last is a diameter of zero, which is a real zero rather than a missing answer.

Formula

d = C ÷ π C = πd

π
About 3.14159. It is not a number anyone chose — it is what every circle's circumference divided by its diameter comes out to, which is why it is what you divide by to go from one to the other
C
The circumference: the distance all the way around the circle, in centimetres. This is the figure you type when you have measured around the edge
d
The diameter: the distance straight across through the centre, in centimetres. This is the figure you type when you have measured across the object
C ÷ π
The direction the page is named for. Dividing a measured circumference by π unwinds the definition and leaves the diameter, which is the measurement most people cannot take directly because it needs the centre
πd
The other direction, and the older form of the relation: the diameter multiplied by π is the distance around. It is the same equation as the first one, rearranged
Both answers printed
Whichever box you filled, the diameter and the circumference are both shown. One of them is always a restatement of what you typed — that is unavoidable when a page answers in both directions at once
Four decimal places
How wide the readings are printed. A diameter worked out from a circumference is a division by an irrational number, so it almost never ends; 20 ÷ π is 6.36619... and the page shows 6.3662

Whenever a circumference has been measured but a diameter is what is needed, or the other way round. The first is by far the commoner: measuring around something with a tape is easy and finding its centre is not. The diameter of a tree trunk, a pipe, a cable, a column, a barrel or a boulder is usually obtained by wrapping a tape around it and dividing, because a caliper that reaches across the middle of a standing object does not exist. Buying is the second use. Stock is sold by one measurement and specified by the other — pipe by outside diameter, hose by bore, bearings by the diameter of the shaft they take, but the thing on the shelf is often measured round — so the conversion happens at the counter. Fitting is the third: a lid, a gasket, a clamp, a hose clip, a belt or a ring has to match a round object whose diameter is what the part is specified in, while the object itself is easiest to measure around. In engineering and drafting it is the difference between the two ways the same hole or shaft is called out, and in machining it is the reason a circumference measurement off a worn part is converted before it is compared with a drawing. In the workshop it sizes a band saw blade or a drive belt from a wrapped tape, and in the kitchen it converts a cake tin's girth into the diameter needed to cut a paper liner. In the classroom it is the demonstration that pi is a ratio rather than a rule: measure around a tin and across it, divide one by the other, and the answer is the same 3.14 for every round object in the room. And in everyday arithmetic it settles questions like whether a round table will fit through a doorway given only its girth, or what diameter of circular rug will cover a floor whose edge length is known.

Worked examples

  1. A circumference of 20

    1. Divide by π: 20 ÷ 3.14159 = 6.36619…
    2. Round to four places: 6.3662

    The pair the page loads with, and the direction the page is named for. The diameter is not a number anyone can write down exactly — it is 20 divided by an irrational constant — which is why the page keeps it unrounded until the end. The overview page prints the same 6.3662 and a radius of 3.1831 for the same circle, and 6.3662 is exactly twice 3.1831.

  2. A diameter of 10

    1. Multiply by π: 10 × 3.14159 = 31.4159
    2. The diameter line repeats the figure you typed, 10

    The reverse direction, and the clearest illustration of what the two-line panel does. The first line is the number you just entered, printed back at you; the answer you wanted is underneath it. This is also a circle of radius 5, and 31.4159 is what the circumference page and the ellipse page both print for that circle.

  3. Back the way you came: a diameter of 6.3662

    1. Multiply by π: 6.3662 × 3.14159 = 20.0000
    2. The answer comes back as 20 exactly, not 19.9999

    The round trip, and the reason the rounding is left to the last step. Type the diameter the page printed for a circumference of 20 back into the diameter box and you land on 20 again. Rounding the diameter before multiplying would have cost a digit here, and a conversion that does not return to where it started is a conversion nobody can chain with anything else.

  4. A circumference of a half centimetre

    1. Divide by π: 0.5 ÷ 3.14159 = 0.15915…
    2. Round to four places: 0.1592

    A small circle, included because this is the size range where four decimals stop being generous. At half a centimetre around, the diameter is a little over a millimetre and a half, and the reading is only just precise enough to be useful. Nothing about the formula changes at this scale — the conversion is the same division it always was.

  5. A circumference of 0

    1. Divide by π: 0 ÷ 3.14159 = 0
    2. Both lines read 0

    A circle with nothing to go around has no width either, and zero is the right pair of answers rather than a missing one. Zero is a legal value in either box — the difference between measuring zero and not measuring at all — and an empty box is the case the page treats as having nothing to work from.

Limitations

This page converts between two measurements of the same circle and gives nothing else: no radius, no area, and no third quantity to check against. If the area is what you need, or the radius, that is another page. Both answers come back in centimetres whatever unit each box is set to, because the conversion happens on the way in; a circumference entered in inches comes back as a centimetre figure that has to be divided by 2.54 to be read in inches, and that single divisor is right for this page only. Whichever box you filled, both lines appear, so one of the two is always a restatement of your own input — the diameter line when you typed a diameter, the circumference line when you typed a circumference. Exactly one box may be filled: give the page two, even two that describe the same circle, and it refuses, because the boxes are two measurements and the page cannot tell which one you meant. The figures are rounded once at the very end, so a hand check that rounds the intermediate radius can differ in the last digit; the page is not the one that is wrong. Four decimal places is a display width and not a claim of exactness. A circumference of zero is accepted and gives a diameter of zero. Nothing here converts between a circumference and an area, and that conversion is not a division by π — it has a square root in it and belongs on an area page.

Frequently asked questions

Why is the first result just the number I typed?
Because the page answers in both directions at once, so one of the two lines is always a restatement of your input. The diameter is the first line, and when you filled the diameter box that line simply echoes it. The figure you asked for is the second one. Which line is the echo changes with the box you filled, which is the price of not putting a mode switch on the page.
Why can I only fill in one of the two boxes?
Because they describe the same circle, so two figures are either redundant or contradictory. A circumference of 20 and a diameter of 7 cannot both be true of one circle, and the page cannot tell which of them you actually measured. Fill in the one you have and leave the other empty, even if you have worked out the other one yourself.
I entered inches. Why are the answers in centimetres?
Because the unit conversion happens on the way in, not on the way out. Your inches are turned into centimetres, the conversion is done, and both figures come back in centimetres. To read them in inches, divide by 2.54. That single divisor is correct here because both quantities are lengths — it would be wrong on an area, where the factor is squared.
Why does dividing by pi not give a round number?
Because pi is irrational, and dividing a tidy number by an irrational one almost never lands on anything tidy. A circumference of 20 gives a diameter of 6.36619..., which the page prints as 6.3662. That is a display width rather than a claim of exactness, and the value behind it has no last digit to find.
If I convert one way and then back, do I get my number again?
Yes, and that is deliberate. The page rounds once at the end rather than at each step, so a diameter of 6.3662 gives a circumference of 20 exactly rather than 19.9999, and a circumference of 31.4159 gives a diameter of 10. A conversion that does not return to where it started cannot be chained with anything else.
Is this the same as the circumference calculator?
No — that page takes a radius or a diameter and gives the circumference, one direction only. This page is the pair on its own, answering both ways, and it is the one to use when the circumference is the measurement you already have. If you want all four quantities at once, the overview page takes any one of them and returns the rest.

References

Related calculators

Circumference CalculatorCircumference of a circle from its radius or diameter.Circle CalculatorRadius, diameter, circumference and area from any one of them.Circle Area CalculatorHow much room there is inside a circle, in square units.Arc Length CalculatorThe length of the arc between two points on a circle.