Enter the numbers from the tire size printed on the sidewall, such as P265/70R17. The calculator finds the diameter, circumference and revolutions. Enter a new wheel diameter (for plus sizing) or a second tire to compare only when you need them.
Enter the width in mm, the aspect ratio in % and the wheel diameter in inches (for P265/70R17, width 265, aspect ratio 70, wheel 17; leave out letters such as P or LT). The new wheel diameter and tire 2 can be left blank.
Result and figure
Enter the numbers from your tire size on the left and press "Calculate". The result will appear here.
Table of Contents
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What you can do on this page
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What is this calculation used for?
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How to Use
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Formulas and figures
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Symbols and terms
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Good to know before you start
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How to calculate it in Excel
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How to calculate it in Google Sheets
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How to calculate it in Python
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How to write it in LaTeX and other math languages (copy and paste)
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How to have ChatGPT do the calculation
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DataChef Features
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Related Features
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NumberChef Calculators List
What you can do on this page
- Enter the numbers from a tire size such as P265/70R17, and you get the overall diameter (tire height), sidewall height, circumference and revolutions on the spot, in inches with millimeters alongside
- Enter a new wheel diameter to get a list of alternative tire sizes whose diameter stays within ±3% of the original tire (for plus sizing or minus sizing)
- Enter two tire sizes to get the difference in each dimension (%) and the speedometer error (a table of what the speedometer shows and your actual speed)
- A plain-language explanation of the formulas and copy-and-paste formulas for Excel, Google Sheets and Python are all on this page
The numbers in a tire size are nominal sizes; the actual dimensions vary a little with the brand, the model, the air pressure and wear. Before changing tire sizes, always check your owner's manual, the tire placard on the driver's door jamb, or a tire shop.
What is this calculation used for?
Checking which sizes fit when plus sizing or changing tires
When you move from 17-inch to 19-inch wheels, keeping the same width and aspect ratio would make the overall diameter much larger; the tire may rub the fender or wheel well, and the speedometer would be off. The basic rule of plus sizing is to choose a tire with a smaller aspect ratio so the diameter stays within ±3% of the original.
For example, going from P265/70R17 (about 31.6 inches tall) to 19-inch wheels, you choose from the sizes within ±3% that also meet your width and model needs. This "match the diameter" calculation is exactly the formulas on this page.
Reading size compatibility when buying winter tires or used tires
Winter tires are often bought one wheel size smaller (minus sizing: a smaller wheel with a taller tire) to save money and add sidewall. Here too, the key question is whether the overall diameter stays about the same; if it does, the effect on the speedometer and ride height stays small.
When you buy used tires or shop online, you cannot see the tire in person. Working out the diameter and width from the tire size and comparing them with your current tires helps you avoid buying tires that do not fit.
Speedometer error, speeding tickets and recorded mileage
After switching to taller tires, the speedometer reads lower than your actual speed. With a tire 3% taller, "60 mph" on the speedometer is really about 62 mph, enough to matter when a police radar checks your speed. With shorter tires, the opposite happens and you drive slower than you think.
The odometer is off by the same ratio, which also matters for lease mileage limits and warranty mileage. Keeping the diameter within ±3% is the practical rule of thumb for keeping these errors small.
Knowing the true mileage and mpg in your records
The odometer adds up distance as "number of tire turns × circumference of the tire it is set for". After changing to a tire with a different diameter, both the recorded miles and the mpg are off by the same ratio.
For example, with a tire whose circumference is 1% shorter, the odometer records about 1% more miles than you actually drove, and your fill-up mpg also looks about 1% better. Knowing the circumference ratio lets you compare fuel records from before and after a tire change correctly.
Everyday work at tire shops and repair shops
At tire shops, auto parts stores and repair shops, questions like "I want bigger wheels" or "which tires fit this wheel?" are answered with exactly the calculations on this page: diameter, diameter difference (%) and speedometer error.
Fitment charts and tire makers' size tables are also built on diameters calculated with these formulas.
Formulas and figures
Sidewall height
Figure
Standard notation
(the usual math form)
In words
(symbols replaced with words)
\(h\)
\(=\)
\(W\)
\(\times\)
\(\dfrac{A}{100}\)
③
\(h\): sidewall height
\(=\)
①
\(W\): tire width
\(\times\)
②
aspect ratio \(A\) ÷ 100
The formula in words
①
Take the
\(W\): tire width
②
multiply it by the
aspect ratio \(A\) divided by 100
③
and you get the
\(h\): sidewall height
Quick example
For P265/70R17 (width 265 mm, aspect ratio 70%), the sidewall height is
\(h\): sidewall height
\(=\)
tire width (265)
\(\times\)
aspect ratio ÷ 100 (0.70)
\(265 \times 0.70 = 185.5\)
Key idea
The aspect ratio tells what percent of the tire's width the sidewall height is. For the same width, a smaller aspect ratio means a thinner (lower) sidewall. A low-profile tire such as a "40 series" makes the wheel look bigger and sportier, while a tall tire such as a "70 series" tends to ride more softly.
The sidewall comes out in millimeters; divide by 25.4 for inches. Here, \(185.5 \div 25.4 \approx 7.3\) inches.
Overall tire diameter
Figure
Standard notation
(the usual math form)
\(D\)
\(=\)
\(R\)
\(\times\)
\(25.4\)
\(+\)
\(2h\)
In words
(symbols replaced with words)
④
\(D\): overall diameter
\(=\)
①
\(R\): wheel diameter (in)
\(\times\)
②
25.4 mm in 1 inch
\(+\)
③
two sidewalls, \(2h\)
The formula in words
①
Take the
\(R\): wheel diameter (in)
②
multiply it by
25.4 mm in 1 inch
to change it to mm,
③
add
two sidewall heights, \(2h\)
④
and you get the
\(D\): overall diameter
Quick example
For P265/70R17 (17-inch wheel, sidewall height 185.5 mm), the overall diameter is
\(D\): overall diameter
\(=\)
wheel diameter (17 in)
\(\times\)
25.4
\(+\)
sidewall (185.5) × 2
\(17 \times 25.4 + 2 \times 185.5 = 431.8 + 371 = 802.8\)
Key idea
Looking at a tire from the side, there is one sidewall above the wheel and one below it. So the overall diameter is "wheel diameter + two sidewalls". In a metric tire size, only the wheel diameter is in inches (a custom used around the world), so multiply it by 25.4 to change it to millimeters before adding.
In the US, the overall diameter is usually quoted in inches as the "tire height": \(802.8 \div 25.4 \approx 31.6\) inches. You can also work in inches from the start: \(17 + 2 \times 7.3 = 31.6\).
Tire circumference
Figure
Standard notation
(the usual math form)
In words
(symbols replaced with words)
\(C\)
\(=\)
\(\pi\)
\(\times\)
\(D\)
③
\(C\): circumference
\(=\)
①
\(\pi\): pi
\(\times\)
②
\(D\): overall diameter
The formula in words
①
Take
\(\pi\): pi (about 3.14)
②
multiply it by the
\(D\): overall diameter
③
and you get the
\(C\): circumference
Quick example
For a tire with an overall diameter of 802.8 mm, the circumference is
\(C\): circumference
\(=\)
pi (3.14159…)
\(\times\)
overall diameter (802.8)
\(3.14159\cdots \times 802.8 \approx 2522\)
Key idea
This is exactly "circumference = π × diameter" from school math. Each time the tire turns once, the car moves forward by the length of the circumference (here about 2.5 m, or about 99.3 inches, a little over 8 feet). This "distance per turn" is the basis of the revolutions and the speedometer calculations that follow.
Revolutions per km (and per mile)
Figure
Standard notation
(the usual math form)
In words
(symbols replaced with words)
\(N\)
\(=\)
\(1{,}000{,}000\)
\(\div\)
\(C\)
③
\(N\): revolutions per km
\(=\)
①
1,000,000 mm in 1 km
\(\div\)
②
\(C\): circumference
The formula in words
①
Take
1,000,000, which is 1 km in mm
②
divide it by the
\(C\): circumference
③
and you get the
\(N\): revolutions per km
Quick example
When a tire with a circumference of 2,522 mm travels 1 km, it turns
\(N\): revolutions per km
\(=\)
1,000,000
\(\div\)
circumference (2,522)
\(1000000 \div 2522 \approx 396.5\)
Key idea
The tire moves forward by one circumference per turn, so dividing 1 km (1,000,000 mm) by the circumference gives the number of turns. The speedometer and odometer count the turns of the tire to show speed and distance, so when the diameter (and therefore the circumference) changes, their readings change too.
US tire makers list "revolutions per mile" instead. One mile is 1,609,344 mm, so divide that by the circumference, or multiply the revolutions per km by 1.609: \(1{,}609{,}344 \div 2522 \approx 638\) revolutions per mile. The calculator above shows revolutions per mile when the units are set to "US customary", and revolutions per km when they are set to "Metric".
Speedometer error (your actual speed)
Figure
Standard notation
(the usual math form)
\(v_2\)
\(=\)
\(v_1\)
\(\times\)
\(\dfrac{C_2}{C_1}\)
In words
(symbols replaced with words)
③
\(v_2\): actual speed
\(=\)
①
\(v_1\): speedometer reading
\(\times\)
②
circumference ratio \(C_2 \div C_1\)
The formula in words
①
Take the
\(v_1\): speedometer reading
②
multiply it by the
ratio of the new tire's circumference \(C_2\) to the circumference the speedometer is set for, \(C_1\)
③
and you get the
\(v_2\): actual speed
Quick example
The speedometer is set for a tire with a circumference of 2,522 mm, but you have switched to a tire with a circumference of 2,501 mm. When the speedometer shows 60 mph, your actual speed is
\(v_2\): actual speed
\(=\)
speedometer reading (60)
\(\times\)
circumference ratio (2501 ÷ 2522)
\(60 \times 2501 \div 2522 \approx 59.5\)
Key idea
The speedometer works out speed as "how fast the tire turns × the circumference of the tire it is set for", so changing to a tire with a different circumference throws the reading off. With a larger tire, the speedometer reads lower than your actual speed (dangerous, because you can speed without noticing); with a smaller tire, it reads higher. The ratio is the same in any unit, so the error in mph is the same percentage as in km/h. Keeping the diameter within ±3% when you change tires keeps this error small.
Tire dimensions come down to two formulas: "sidewall = width × aspect ratio ÷ 100" and "diameter = wheel diameter × 25.4 + two sidewalls". Once you know the circumference (π × diameter), the revolutions and the speedometer error take only division and ratios. Divide any result in millimeters by 25.4 to get inches.
Symbols and terms
Symbols
| \(W\) | Tire width (section width). The first number in the tire size, in mm. It is the nominal section width; the actual width varies a little with the tire model and the rim width. (For P265/70R17, \(W = 265\).) |
| \(A\) | Aspect ratio. The sidewall height as a percent of the width, the number after the slash in the tire size. (For P265/70R17, \(A = 70\).) |
| \(h\) | Sidewall height (mm), found with \(h = W \times A \div 100\). |
| \(R\) | Wheel (rim) diameter. The number after the R in the tire size, in inches. (For P265/70R17, \(R = 17\).) |
| \(D\) | Overall diameter (mm). The diameter of the tire seen from the side, also called the tire height. |
| \(C\) | Circumference (mm). The distance the tire travels in one turn. |
| \(N\) | Revolutions per km, how many times the tire turns while traveling 1 km (multiply by 1.609 for revolutions per mile). |
| \(\pi\) | Pi, about 3.14159. The constant that tells how many times the diameter the circumference is. |
| \(v_1,\ v_2\) | \(v_1\) is the speedometer reading and \(v_2\) is the actual speed (both in mph, or both in km/h). They are used to find how far off the speedometer is after a tire change. |
Terms
| tire size | The size code on the sidewall, such as P265/70R17: width (mm) / aspect ratio (%), R for radial construction, then the wheel diameter (inches). A leading P means a passenger-car tire (P-metric), LT means a light-truck tire, and no letter means a Euro-metric tire; the dimensions are read the same way. A real tire shows more, such as "P265/70R17 113T", where 113 is the load index and T is the speed rating (not used for the dimensions here). Some off-road tires use flotation sizes such as 33x12.50R15, which give the diameter directly in inches; this calculator is for metric sizes. |
| aspect ratio | The sidewall height as a percent of the tire width, also called the series or profile. The smaller the number, the thinner (lower-profile) the tire. |
| sidewall | The rubber side of the tire, from the edge of the wheel to the tread that touches the road. Its height helps decide the overall diameter. |
| wheel diameter (rim diameter) | The diameter of the wheel the tire fits on. In tire sizes it is always given in inches (1 inch = 25.4 mm), around the world. |
| inch | A unit of length. 1 inch = 25.4 mm exactly. In the US, tire height and wheel size are both talked about in inches. |
| plus sizing | Changing to wheels with a larger diameter ("plus one" for 1 inch larger, "plus two" for 2 inches). To keep the overall diameter the same, you switch to a tire with a smaller aspect ratio (a thinner sidewall). Going to smaller wheels is called minus sizing. |
| speedometer error | The gap between the speed on the speedometer and your actual speed. The speedometer calculates speed from how fast the tire turns, so a tire with a different diameter (circumference) creates a gap. |
Good to know before you start
Here is what helps you use the calculation on this page with real understanding, not just by pressing the button.
| Percents (Grade 6) |
|
| Circumference and pi (Grade 7) |
|
| Converting units (Grades 5–7) |
|
| Ratios (Grade 6) |
|
How to calculate it in Excel
Copy the whole table below and paste it into cell A1 in Excel. It works as is.
Table to find the sidewall height
| Tire width W (mm) | 265 |
| Aspect ratio A (%) | 70 |
| Sidewall height h (mm) | =B1*B2/100 |
Table to find the overall diameter
| Wheel diameter R (in) | 17 |
| Sidewall height h (mm) | 185.5 |
| Overall diameter D (mm) | =B1*25.4+2*B2 |
Table to find the circumference
| Overall diameter D (mm) | 802.8 |
| Circumference C (mm) | =PI()*B1 |
Table to find the revolutions per km
| Circumference C (mm) | 2522 |
| Revolutions per km N | =1000000/B1 |
Table to find the speedometer error
| Speedometer reading v1 (mph) | 60 |
| Circumference the speedometer is set for C1 (mm) | 2522 |
| Circumference of your tire C2 (mm) | 2501 |
| Actual speed v2 (mph) | =B1*B3/B2 |
After pasting, the upper cells in column B are your inputs and the last row is calculated automatically.
"*" is multiplication and "/" is division, and PI() is the Excel function that returns pi.
For example, the first table shows 185.5 in B3, the second shows 802.8 in B3, the third shows about 2522.07 in B2, the fourth shows about 396.51 in B2, and the fifth shows about 59.50 in B4. To get inches, divide any millimeter value by 25.4 (add a cell such as =B3/25.4). Just replace the numbers in column B with the values from your tire size.
"*" is multiplication and "/" is division, and PI() is the Excel function that returns pi.
For example, the first table shows 185.5 in B3, the second shows 802.8 in B3, the third shows about 2522.07 in B2, the fourth shows about 396.51 in B2, and the fifth shows about 59.50 in B4. To get inches, divide any millimeter value by 25.4 (add a cell such as =B3/25.4). Just replace the numbers in column B with the values from your tire size.
How to calculate it in Google Sheets
Copy the whole table below and paste it into cell A1 in Google Sheets. It works as is.
Table to find the sidewall height
| Tire width W (mm) | 265 |
| Aspect ratio A (%) | 70 |
| Sidewall height h (mm) | =B1*B2/100 |
Table to find the overall diameter
| Wheel diameter R (in) | 17 |
| Sidewall height h (mm) | 185.5 |
| Overall diameter D (mm) | =B1*25.4+2*B2 |
Table to find the circumference
| Overall diameter D (mm) | 802.8 |
| Circumference C (mm) | =PI()*B1 |
Table to find the revolutions per km
| Circumference C (mm) | 2522 |
| Revolutions per km N | =1000000/B1 |
Table to find the speedometer error
| Speedometer reading v1 (mph) | 60 |
| Circumference the speedometer is set for C1 (mm) | 2522 |
| Circumference of your tire C2 (mm) | 2501 |
| Actual speed v2 (mph) | =B1*B3/B2 |
The same formulas as in Excel work as is. Copy the whole table, paste it into cell A1, and replace the numbers in column B with the values from your tire size.
How to calculate it in Python
import math
tire_width_mm = 265 # tire width (mm)
aspect_ratio_pct = 70 # aspect ratio (%)
rim_diameter_inch = 17 # wheel diameter (inches)
sidewall_mm = tire_width_mm * aspect_ratio_pct / 100 # sidewall height
diameter_mm = rim_diameter_inch * 25.4 + 2 * sidewall_mm # overall diameter
circumference_mm = math.pi * diameter_mm # circumference
revolutions_per_km = 1000000 / circumference_mm # revolutions per km
revolutions_per_mile = 1609344 / circumference_mm # revolutions per mile (1 mile = 1,609,344 mm)
print(f"Sidewall height: {sidewall_mm:.1f} mm ({sidewall_mm / 25.4:.1f} in)")
print(f"Overall diameter: {diameter_mm:.1f} mm ({diameter_mm / 25.4:.1f} in)")
print(f"Circumference: {circumference_mm:.0f} mm")
print(f"Revolutions per km: {revolutions_per_km:.1f}")
print(f"Revolutions per mile: {revolutions_per_mile:.1f}")
Runs with the standard library only. math.pi is pi. Replace the first three numbers with the values from your tire size and run it.
How to write it in LaTeX and other math languages (copy and paste)
Sidewall height
h = W × A ÷ 100
h = W \times \dfrac{A}{100}
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>h</mi>
<mo>=</mo>
<mi>W</mi>
<mo>×</mo>
<mfrac><mi>A</mi><mn>100</mn></mfrac>
</mrow>
</math>
h = W xx A/100
h = W*(A/100)
h := W*A/100;
h = W*A/100;
h = W(A/100)
Overall tire diameter
D = R × 25.4 + 2h
D = R \times 25.4 + 2h
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>D</mi>
<mo>=</mo>
<mi>R</mi>
<mo>×</mo>
<mn>25.4</mn>
<mo>+</mo>
<mn>2</mn>
<mi>h</mi>
</mrow>
</math>
D = R xx 25.4 + 2h
d = R*25.4 + 2*h
d := R*25.4 + 2*h;
D = R*25.4 + 2*h;
D = 25.4R + 2h
Tire circumference
C = πD
C = \pi D
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>C</mi>
<mo>=</mo>
<mi>π</mi>
<mi>D</mi>
</mrow>
</math>
C = pi D
c = Pi*d
C := Pi*d;
C = pi*D;
C = πD
Revolutions per km (and per mile)
N = 1000000 ÷ C
N = \dfrac{1{,}000{,}000}{C}
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>N</mi>
<mo>=</mo>
<mfrac><mn>1000000</mn><mi>C</mi></mfrac>
</mrow>
</math>
N = 1000000 / C
n = 1000000/c
N := 1000000/C;
N = 1000000/C;
N = 1000000/C
Speedometer error (your actual speed)
v₂ = v₁ × C₂ ÷ C₁
v_2 = v_1 \times \dfrac{C_2}{C_1}
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<msub><mi>v</mi><mn>2</mn></msub>
<mo>=</mo>
<msub><mi>v</mi><mn>1</mn></msub>
<mo>×</mo>
<mfrac>
<msub><mi>C</mi><mn>2</mn></msub>
<msub><mi>C</mi><mn>1</mn></msub>
</mfrac>
</mrow>
</math>
v_2 = v_1 xx C_2/C_1
v2 = v1*(C2/C1)
v2 := v1*C2/C1;
v2 = v1*C2/C1;
v2 = v1(C2/C1)
How to have ChatGPT do the calculation
You are a tire size calculation assistant. Do the following calculation by actually running Python code, and base your answer only on the numbers from the execution result (do not answer by mental math or guessing). For a tire of size P265/70R17 (width 265 mm, aspect ratio 70%, wheel diameter 17 inches), find each of the following: 1. The sidewall height (mm and inches) = width × aspect ratio ÷ 100 2. The overall diameter (mm and inches) = wheel diameter × 25.4 + sidewall height × 2 3. The circumference (mm) = pi × overall diameter 4. The revolutions per mile = 1,609,344 ÷ circumference (1 mile = 1,609,344 mm) Show the formulas you used and the numbers from the execution result.
How to Use
-
1Enter your numbersType the numbers you want to calculate with into the input fields
-
2CalculatePress the "Calculate" button
-
3Check the resultThe result appears on the spot. The same page also explains the idea behind the calculation and the formula
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