Choose what you want to calculate and enter the numbers. The scale factor m : n is in the order "Figure ① : Figure ②".
Enter numbers only. Decimals and fractions such as 3/4 are OK (numbers greater than 0 only). A scale factor such as 1.5 : 2 is rewritten in simplest whole-number form before calculating.
Result and figure
Enter the scale factor in the fields on the left and press "Calculate". The result and a figure will appear here.
Table of Contents
-
What you can do on this page
-
What is this calculation used for?
-
How to Use
-
Formulas and figures
-
Symbols and terms
-
Good to know before you start
-
How to calculate it in Excel
-
How to calculate it in Google Sheets
-
How to calculate it in Python
-
How to write it in LaTeX and other math languages (copy and paste)
-
How to have ChatGPT do the calculation
-
DataChef Features
-
Related Features
-
NumberChef Calculators List
What you can do on this page
- Enter a scale factor \(m : n\), and you get the area ratio \(m^2 : n^2\) and the volume ratio \(m^3 : n^3\) on the spot. Ratios with decimals or fractions, such as 1.5 : 2, are rewritten in simplest whole-number form, such as 3 : 4
- From the scale factor and the length, area or volume of one figure, it finds the matching value for the other figure. The answer is shown both as an exact fraction in lowest terms, such as \(\dfrac{21}{2}\), and as a decimal
- It also handles map scales such as 1:24,000: map distance → actual distance, and actual distance → map distance, including unit conversion between inches, feet and miles (or cm, m and km)
- Formulas and figures explain why squaring the scale factor gives the area ratio and cubing it gives the volume ratio
- The result shows a figure of the two similar shapes (or, for map scales, a diagram of how the conversion works), so you can see the ratios at a glance
Enter numbers greater than 0 for the scale factor, lengths, areas, volumes and the scale denominator (side lengths and areas of similar figures are always positive).
What is this calculation used for?
Reading actual distances on a map (hiking, walking and emergency planning)
On a 1:25,000 topographic map, 4 cm on the map is 1 km in reality (4 × 25,000 = 100,000 cm). US Geological Survey topo maps use 1:24,000, where 1 inch on the map is 24,000 inches, or 2,000 feet. Measure a route on the map and multiply by the scale denominator, and you get a good idea of how far you will walk.
The same scale calculation is used to estimate the distance from your home to a shelter on an evacuation or flood map.
Sizes of scale models and miniatures (scale and similarity)
The "1:144" on a plastic model kit, "1:160" for N scale model trains or "1:87" for HO scale is the scale itself. An 80-foot passenger car in N scale is 80 ft = 960 in, and 960 ÷ 160 = 6 in long. Designing a model is a chain of calculations that make scale drawings and reduced solids similar to the real thing.
Changing the size of a cake pan (area and volume ratios)
To make a recipe for an 8-inch round pan in a 10-inch round pan, the ratio of the diameters is 8 : 10 = 4 : 5. If the pan is also deeper in the same proportion (a similar pan), scale the ingredients by the volume ratio \(4^3 : 5^3 = 64 : 125\) (about 1.95 times). If the pans are the same depth, only the bottom area grows, so use the area ratio \(4^2 : 5^2 = 16 : 25\) (about 1.56 times).
Knowing that "a small change in length makes a big change in amount, squared or cubed" helps you avoid kitchen mistakes.
Enlarging photos and copies (area ratio)
Enlarging a 4 × 6 inch photo to 8 × 12 inches doubles every length (a scale factor of 1 : 2), so the area becomes \(2^2 = 4\) times as large. That is why "doubling the size of a poster used four times the paper and ink".
In most countries outside the US, paper sizes are designed so that two A4 sheets make exactly one A3 sheet. The area ratio is \(1 : 2\), so the length ratio (the scale factor) is its square root, \(1 : \sqrt{2}\). That is why the "141%" copier button (\(\sqrt{2} \approx 1.41\)) enlarges A4 to A3.
Limits on the size of animals and buildings (the square-cube law)
If an animal's body keeps almost the same shape while its lengths double, the cross-section of its bones (the source of their strength) grows only \(2^2 = 4\) times, while its weight (volume) grows \(2^3 = 8\) times. This "square-cube law" is why larger animals have thicker, sturdier legs.
It is also one reason why, in building and machine design, something that worked as a model can break at full size: area and volume grow at different rates.
Formulas and figures
Scale factor and corresponding side lengths
Standard notation
(the usual math form)
\(b\)
\(=\)
\(a\)
\(\times\)
\(\dfrac{n}{m}\)
In words
(symbols replaced with words)
③
\(b\): corresponding side of Figure ②
\(=\)
①
\(a\): side of Figure ①
\(\times\)
②
\(\dfrac{n}{m}\): multiplier from the scale factor
The formula in words
①
For similar figures with a scale factor of \(m : n\), take the
\(a\): side of Figure ①
②
multiply it by the
\(\dfrac{n}{m}\): multiplier from the scale factor (\(n\) divided by \(m\))
③
and you get the
\(b\): corresponding side of Figure ②
Quick example
For similar figures with a scale factor of \(2 : 3\), if a side of Figure ① is \(12\) in long, the corresponding side of Figure ② is
corresponding side of Figure ②
\(=\)
side of Figure ① (12 in)
\(\times\)
multiplier \(\dfrac{3}{2}\)
\(b = 12 \times \dfrac{3}{2} = 18\)
Key idea
In similar figures, the ratio of any pair of corresponding sides is the same scale factor \(m : n\). So the length in Figure ② is "the length in Figure ① × \(\dfrac{n}{m}\)" (to go from Figure ② back to Figure ①, multiply by \(\dfrac{m}{n}\) instead).
Not just sides: every kind of length, such as the perimeter, a diagonal or a height, keeps the scale factor \(m : n\) as is.
Area ratio of similar figures (scale factor squared)
Figure
Standard notation
(the usual math form)
\(S_{1} : S_{2}\)
\(=\)
\(m\)
\(2\)
\(:\)
\(n\)
\(2\)
In words
(symbols replaced with words)
④
area ratio (area of Figure ① to area of Figure ②)
\(=\)
①
\(m\): scale factor term for Figure ①
③
squared
\(:\)
②
\(n\): scale factor term for Figure ②
squared
The formula in words
①
Take the scale factor \(m : n\):
\(m\): the Figure ① term
②
and
\(n\): the Figure ② term
③
square each one
④
and you get the
area ratio \(S_1 : S_2\)
Quick example
The area ratio of similar figures with a scale factor of \(2 : 3\) is
area ratio
\(=\)
\(2^2 = 4\)
\(:\)
\(3^2 = 9\)
\(S_{1} : S_{2} = 2^{2} : 3^{2} = 4 : 9\)
Key idea
Why the area ratio is squared: a scale factor of \(m : n\) means Figure ② is Figure ① enlarged (or reduced) by \(\dfrac{n}{m}\) both across and up. Area is found by multiplying two lengths, like "width × height", so the factor \(\dfrac{n}{m}\) is applied twice and the area changes by \(\left(\dfrac{n}{m}\right)^2\). As in the figure above, for rectangles with a scale factor of \(1 : 2\), exactly \(4 = 2^2\) copies of the small one fit into the large one.
For shapes other than rectangles, such as triangles and circles, the same thing holds if you think of them as made of tiny grid squares. So for any similar figures, the area ratio is \(m^2 : n^2\). The surface areas of similar solids are also areas, so their ratio is \(m^2 : n^2\) too.
Volume ratio of similar solids (scale factor cubed)
Standard notation
(the usual math form)
\(V_{1} : V_{2}\)
\(=\)
\(m\)
\(3\)
\(:\)
\(n\)
\(3\)
In words
(symbols replaced with words)
④
volume ratio (volume of solid ① to volume of solid ②)
\(=\)
①
\(m\): scale factor term for solid ①
③
cubed
\(:\)
②
\(n\): scale factor term for solid ②
cubed
The formula in words
①
Take the scale factor \(m : n\):
\(m\): the solid ① term
②
and
\(n\): the solid ② term
③
cube each one
④
and you get the
volume ratio \(V_1 : V_2\)
Quick example
The volume ratio of similar solids with a scale factor of \(2 : 3\) is
volume ratio
\(=\)
\(2^3 = 8\)
\(:\)
\(3^3 = 27\)
\(V_{1} : V_{2} = 2^{3} : 3^{3} = 8 : 27\)
Key idea
The volume ratio is cubed for the same reason the area ratio is squared. Volume is found by multiplying three lengths, like "length × width × height", so the multiplier \(\dfrac{n}{m}\) is applied three times and the volume changes by \(\left(\dfrac{n}{m}\right)^3\).
For example, exactly \(8 = 2^3\) of the original cube fit into a cube with sides twice as long. Remember them as a set, "lengths to the 1st power, areas squared, volumes cubed", and you will not get confused on a test or in real life.
Map scale and actual distance
Standard notation
(the usual math form)
\(L\)
\(=\)
\(\ell\)
\(\times\)
\(d\)
In words
(symbols replaced with words)
③
\(L\): actual distance
\(=\)
①
\(\ell\): map distance
\(\times\)
②
\(d\): scale denominator
The formula in words
①
On a map with a scale of \(1 : d\), take the
\(\ell\): map distance
②
multiply it by the
\(d\): scale denominator (such as 24000)
③
and you get the
\(L\): actual distance
Quick example
On a map with a scale of \(1 : 24000\), if the map distance is \(3\) in, the actual distance is
actual distance
\(=\)
map distance (3 in)
\(\times\)
scale denominator (24000)
\(L = 3 \times 24000 = 72000\)
\(72000\ \mathrm{in} = 6000\ \mathrm{ft} \approx 1.14\ \mathrm{mi}\)
Key idea
A map with a scale of \(1 : 24000\) (also written \(\dfrac{1}{24000}\)) is a scale drawing of the real land, shrunk to \(\dfrac{1}{24000}\) of its size. So the map and the real land have a scale factor of \(1 : 24000\), and the formula for corresponding sides (the first formula) works as is.
To go the other way, from actual distance to map distance, divide by the scale denominator (\(\ell = L \div d\)).
Do not forget to convert units: \(1\) ft \(= 12\) in, and \(1\) mi \(= 5280\) ft \(= 63360\) in. The usual approach is to calculate in inches first and then convert to feet or miles. On a \(1 : 24000\) topographic map, 1 inch on the map is 24,000 inches, or 2,000 feet, and on a \(1 : 63360\) map, 1 inch is exactly 1 mile. The same idea works with metric units: on a \(1 : 25000\) map, 4 cm is \(100000\) cm \(= 1\) km.
For similar figures with a scale factor of \(m : n\), the ratio of corresponding sides and all other lengths stays \(m : n\), the area ratio is its square \(m^2 : n^2\), and the volume ratio is its cube \(m^3 : n^3\). A map scale of \(1 : d\) makes the map a scale drawing with a scale factor of \(1 : d\) to the real land, so the actual distance is "map distance × \(d\)".
Symbols and terms
Symbols
| \(m,\ n\) | m, n | The two numbers of the scale factor. On this page, \(m\) is for Figure ① and \(n\) is for Figure ②. A ratio of whole numbers is the usual form, but a ratio such as 1.5 : 2 can also be rewritten in simplest whole-number form (3 : 4 in this example). |
| \(:\) | to | The symbol for a ratio. \(2 : 3\) is read "2 to 3", and it says that two amounts compare as 2 compares to 3. |
| \(a,\ b\) | a, b | Lengths of corresponding sides: \(a\) is a side of Figure ① and \(b\) is the corresponding side of Figure ②. Letters near the start of the alphabet are usually used for fixed lengths. |
| \(S_1,\ S_2\) | S sub 1, S sub 2 | The areas of Figure ① and Figure ②. \(S\) is often used for area; it is said to come from "square" or "surface". The small number at the lower right (the subscript) tells which figure it is. |
| \(V_1,\ V_2\) | V sub 1, V sub 2 | The volumes of solid ① and solid ②. \(V\) is the first letter of "volume". |
| \(m^2\) | m squared | \(m\) multiplied by itself (\(m^2 = m \times m\)), called "m squared" or "m to the second power". The area ratio is the scale factor squared. |
| \(m^3\) | m cubed | Three factors of \(m\) multiplied together (\(m^3 = m \times m \times m\)), called "m cubed" or "m to the third power". The volume ratio is the scale factor cubed. |
| \(\ell\) | ell | The map distance. It is a script form of l, from "length", used so it is not confused with the number 1 or a capital I. |
| \(L\) | capital L | The actual distance. It is a capital letter to tell it apart from the map distance \(\ell\). |
| \(d\) | d | The scale denominator. For a scale of \(1 : 24000\) (\(\dfrac{1}{24000}\)), \(d = 24000\). It comes from the first letter of "denominator". |
Terms
| similar figures | Two figures with the same shape but possibly different sizes. Enlarging or reducing one makes it fit exactly on the other. It is written with the symbol ~, as in \(\triangle ABC \sim \triangle DEF\). |
| scale factor | The ratio of the lengths of corresponding sides of two similar figures. It is the same whichever pair of corresponding sides you take. It is written as a ratio \(m : n\) or as a single multiplier \(\dfrac{n}{m}\). |
| corresponding sides | In two similar (or congruent) figures, the sides that are in matching positions. In similar figures, the ratios of the lengths of all corresponding sides are equal. |
| area ratio | The ratio of the areas of two figures. For similar figures, it is the scale factor \(m : n\) squared, \(m^2 : n^2\). |
| volume ratio | The ratio of the volumes of two solids. For similar solids, it is the scale factor \(m : n\) cubed, \(m^3 : n^3\). |
| surface area | The total area of the outside of a solid. It is a kind of area, so the ratio of the surface areas of similar solids is the same as the area ratio, \(m^2 : n^2\). |
| map scale | How much the real thing was shrunk to make a map or plan. It is written as a ratio such as 1 : 25,000 or a fraction such as \(\dfrac{1}{25000}\). A map with a scale of 1 : 25,000 is a scale drawing with a scale factor of \(1 : 25000\) to the real land. |
| scale drawing | A drawing reduced (or enlarged) without changing its shape. Scale drawings are taught in Grade 7, and similar figures in Grade 8 and Geometry put the same idea into mathematical language. |
| enlargement | A figure made larger without changing its shape (also called a dilation with a scale factor greater than 1). It is the opposite of a reduction. |
| simplify a ratio | To rewrite a ratio with the smallest possible whole numbers. Divide both terms by their greatest common factor (for example, \(12 : 18 = 2 : 3\)). For a ratio with decimals or fractions, first multiply both terms to make whole numbers, then simplify (for example, \(1.5 : 2 = 3 : 4\)). |
| greatest common factor (GCF) | The largest number that divides two or more whole numbers evenly. To simplify a ratio, divide both terms by this number. |
| power | A number multiplied by itself repeatedly. In \(2^3 = 2 \times 2 \times 2 = 8\), the small raised number (the exponent) tells how many times it is used as a factor. |
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.
If you get stuck, going back to the topics in this list is the quickest way forward.
| Ratios (Grade 6) |
|
| Scale drawings (Grade 7) |
|
| Exponents (Grade 6) |
|
| Multiplying and dividing fractions (Grades 5–6) |
|
| Converting units of length (Grades 4–5) |
|
| Similar figures (Grade 8 and Geometry) |
|
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 area and volume ratios from the scale factor
| Scale factor m (Figure ①) | 2 |
| Scale factor n (Figure ②) | 3 |
| Area ratio, Figure ① term m² | =B1^2 |
| Area ratio, Figure ② term n² | =B2^2 |
| Volume ratio, Figure ① term m³ | =B1^3 |
| Volume ratio, Figure ② term n³ | =B2^3 |
Table to convert a length, area or volume with the scale factor (area example)
| Scale factor m (Figure ①) | 3 |
| Scale factor n (Figure ②) | 5 |
| Area of Figure ① | 18 |
| Area of Figure ② (×(n/m)²) | =B3*(B2/B1)^2 |
Table to find the actual distance from a map scale
| Scale denominator (the 63360 in 1:63360) | 63360 |
| Map distance (in) | 4 |
| Actual distance (in) | =B1*B2 |
| Actual distance (ft) | =B3/12 |
| Actual distance (mi) | =B3/63360 |
Table to find the map distance from the actual distance
| Scale denominator (the 24000 in 1:24000) | 24000 |
| Actual distance (mi) | 3 |
| Actual distance (in) | =B2*63360 |
| Map distance (in) | =B3/B1 |
After pasting, the upper rows are your inputs and the lower rows are calculated automatically. "^" raises to a power, "*" is multiplication and "/" is division.
The first table is for a scale factor of 2 : 3, and it gives the area ratio 4 and 9 and the volume ratio 8 and 27. Enter the scale factor as whole numbers (for a ratio such as 1.5 : 2, the results are easier to read if you first rewrite it as whole numbers, such as 3 : 4 by doubling both terms).
The second table is for a scale factor of 3 : 5 with an area of 18 for Figure ①, and the area of Figure ② comes out as 50. To convert a length, remove "^2"; for a volume, change it to "^3".
The third table is for 4 in on a 1:63,360 map (1 inch = 1 mile). The actual distance is 253,440 in = 21,120 ft = 4 mi.
The fourth table puts an actual distance of 3 mi on a 1:24,000 topographic map. The map distance is 7.92 in (1 mi = 63,360 in).
The first table is for a scale factor of 2 : 3, and it gives the area ratio 4 and 9 and the volume ratio 8 and 27. Enter the scale factor as whole numbers (for a ratio such as 1.5 : 2, the results are easier to read if you first rewrite it as whole numbers, such as 3 : 4 by doubling both terms).
The second table is for a scale factor of 3 : 5 with an area of 18 for Figure ①, and the area of Figure ② comes out as 50. To convert a length, remove "^2"; for a volume, change it to "^3".
The third table is for 4 in on a 1:63,360 map (1 inch = 1 mile). The actual distance is 253,440 in = 21,120 ft = 4 mi.
The fourth table puts an actual distance of 3 mi on a 1:24,000 topographic map. The map distance is 7.92 in (1 mi = 63,360 in).
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 area and volume ratios from the scale factor
| Scale factor m (Figure ①) | 2 |
| Scale factor n (Figure ②) | 3 |
| Area ratio, Figure ① term m² | =B1^2 |
| Area ratio, Figure ② term n² | =B2^2 |
| Volume ratio, Figure ① term m³ | =B1^3 |
| Volume ratio, Figure ② term n³ | =B2^3 |
Table to convert a length, area or volume with the scale factor (area example)
| Scale factor m (Figure ①) | 3 |
| Scale factor n (Figure ②) | 5 |
| Area of Figure ① | 18 |
| Area of Figure ② (×(n/m)²) | =B3*(B2/B1)^2 |
Table to find the actual distance from a map scale
| Scale denominator (the 63360 in 1:63360) | 63360 |
| Map distance (in) | 4 |
| Actual distance (in) | =B1*B2 |
| Actual distance (ft) | =B3/12 |
| Actual distance (mi) | =B3/63360 |
Table to find the map distance from the actual distance
| Scale denominator (the 24000 in 1:24000) | 24000 |
| Actual distance (mi) | 3 |
| Actual distance (in) | =B2*63360 |
| Map distance (in) | =B3/B1 |
The same formulas as in Excel work as is. Copy the whole table, paste it into cell A1, and replace the scale factor or lengths with your own numbers.
How to calculate it in Python
from fractions import Fraction
# Scale factor m : n (Figure ① : Figure ②). Decimals such as 1.5 can be written as is
ratio_m = Fraction('1.5')
ratio_n = Fraction('2')
# Rewrite in simplest whole-number form (reducing m ÷ n gives numerator : denominator as whole numbers)
reduced = ratio_m / ratio_n
int_m, int_n = reduced.numerator, reduced.denominator
print(f"Scale factor: {int_m} : {int_n}")
print(f"Area ratio: {int_m ** 2} : {int_n ** 2}")
print(f"Volume ratio: {int_m ** 3} : {int_n ** 3}")
# Area of Figure ② from the scale factor and the area of Figure ① (areas use the scale factor squared)
area_of_first = Fraction(18)
area_of_second = area_of_first * (ratio_n / ratio_m) ** 2
print(f"Area of Figure ②: {area_of_second} = {float(area_of_second)}")
With the fractions module from the standard library, you can calculate with exact fractions and no decimal rounding error. This example is for a scale factor of 1.5 : 2. When you run it, it shows the scale factor "3 : 4", the area ratio "9 : 16", the volume ratio "27 : 64", and, for an area of 18 for Figure ①, the area of Figure ② "32 = 32.0". Change the scale factor and the area and run it. To convert a length, remove "** 2"; for a volume, change it to "** 3".
How to write it in LaTeX and other math languages (copy and paste)
Scale factor and corresponding side lengths
b = a × n/m
b = a \times \dfrac{n}{m}
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>b</mi>
<mo>=</mo>
<mi>a</mi>
<mo>×</mo>
<mfrac><mi>n</mi><mi>m</mi></mfrac>
</mrow>
</math>
b = a xx n/m
b = a*(n/m)
b := a*n/m;
b = a*n/m;
b = a(n/m)
Area ratio of similar figures (scale factor squared)
S₁ : S₂ = m² : n²
S_{1} : S_{2} = m^{2} : n^{2}
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<msub><mi>S</mi><mn>1</mn></msub>
<mo>:</mo>
<msub><mi>S</mi><mn>2</mn></msub>
<mo>=</mo>
<msup><mi>m</mi><mn>2</mn></msup>
<mo>:</mo>
<msup><mi>n</mi><mn>2</mn></msup>
</mrow>
</math>
S_1 : S_2 = m^2 : n^2
S1/S2 == m^2/n^2
S1/S2 = m^2/n^2;
S1/S2 == m^2/n^2
S_1 : S_2 = m^2 : n^2
Volume ratio of similar solids (scale factor cubed)
V₁ : V₂ = m³ : n³
V_{1} : V_{2} = m^{3} : n^{3}
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<msub><mi>V</mi><mn>1</mn></msub>
<mo>:</mo>
<msub><mi>V</mi><mn>2</mn></msub>
<mo>=</mo>
<msup><mi>m</mi><mn>3</mn></msup>
<mo>:</mo>
<msup><mi>n</mi><mn>3</mn></msup>
</mrow>
</math>
V_1 : V_2 = m^3 : n^3
V1/V2 == m^3/n^3
V1/V2 = m^3/n^3;
V1/V2 == m^3/n^3
V_1 : V_2 = m^3 : n^3
Map scale and actual distance
L = ℓ × d
L = \ell \times d
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>L</mi>
<mo>=</mo>
<mi>ℓ</mi>
<mo>×</mo>
<mi>d</mi>
</mrow>
</math>
L = l xx d
L = l*d
L := l*d;
L = l*d;
L = ℓ × d
How to have ChatGPT do the calculation
You are a math (similar figures) 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 similar figures with a scale factor of 1.5 : 2, show each of the following: 1. The scale factor in simplest whole-number form 2. The area ratio (scale factor squared) and the volume ratio (scale factor cubed), both as whole-number ratios 3. The area of Figure ② when the area of Figure ① is 18 in² Also, on a map with a scale of 1:24,000, find how many feet and how many miles 5 inches on the map is in reality. In Python, use the fractions module from the standard library to calculate exactly, and 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
DataChef Features
Easy and Free
Unlimited conversions for free.
No technical knowledge required.
Intuitive and user-friendly operation.
No technical knowledge required.
Intuitive and user-friendly operation.
No Registration Required
Available immediately after access.
Can be used without registering personal information.
Can be used without registering personal information.
Safe and Secure
Fully SSL encrypted communication.
Automatic file deletion by clicking "download".
Automatic file deletion by clicking "download".
Fast
High-speed site access
and rapid file conversion.
and rapid file conversion.
No Watermark
No watermark.
No attribution required.
No attribution required.
Commercial Use Available
Free for commercial use.
No need to contact us for commercial use permission.
No need to contact us for commercial use permission.
Related Features
Ratio and Proportion Calculator (Solve A:B = C:D, Scale a Ratio)
Solves for the unknown in a proportion such as "3 : 4 = 600 : ?" with cross multiplication
Polygon Angle Calculator (Sum of Interior and Exterior Angles, Regular Polygons)
Finds the interior and exterior angle sums of an n-gon and each angle of a regular n-gon, with a figure that splits it into triangles
Direct and Inverse Variation Calculator (Equation and Constant of Variation from One Point)
From one point on the graph, finds the equation of direct variation y=ax or inverse variation y=a/x and the constant a, with steps and a graph
Ad 
