If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Main content

Interpreting a scale drawing

Understand how a scale drawing is converted into real numbers using the scale factor. Created by Sal Khan.

Want to join the conversation?

  • winston baby style avatar for user Kantavitch I.
    i confused why it must be 1:80 can it be 80:1
    (58 votes)
    Default Khan Academy avatar avatar for user
    • aqualine ultimate style avatar for user Gaurang Bhana
      The ratio always comes in this order

      Drawing to Reality

      This means that for every 1 cm on the drawing, there is 80 cm in reality. To put it another way, take this

      1:80 means that the building is 80 times the size of the drawing
      80:1 means that the drawing is 80 times the size of the building

      If it were 80:1, the drawing itself would be over 100m long.
      (21 votes)
  • leafers ultimate style avatar for user Elyuz Lukes
    Couldn't you just leave it in centimeters?
    (31 votes)
    Default Khan Academy avatar avatar for user
  • piceratops seedling style avatar for user isaaccijntje
    I still don't get the meters part but I understand the centimeter part perfectly.
    (2 votes)
    Default Khan Academy avatar avatar for user
    • aqualine ultimate style avatar for user Robby Olivam
      Meters and centimeters are similar to feet and inches in the English system. There are 100 centimeters in every meter, just as there are 12 inches in every foot. The tricky thing is that there are 10,000 square centimeters in one square meter, and 144 square inches in one square foot.

      Think of a floor tile that is one square foot. The width and height of the tile would both be 12 inches. Because the area of a rectangle = length * width, we would multiply 12 * 12 to get 144 square inches in that one square foot. I would recommend drawing it out for yourself if you still have trouble with that part.

      If this didn't help, and you're still having trouble with this problem, let me know and I can try to find a better way of explaining it.
      (17 votes)
  • leafers ultimate style avatar for user BorkusMalorkus5
    This is the first video in this series, (Scale Drawings) and it operates through a ratio e.g. 1:80 But Sal never defines what either of these numbers are?? Which is which? I'm finding this very hard to understand despite the already present clarification on the video which states that the ration should be 1:80 not 80:1.

    Sal still uses 80 in his multiplication and I am confused as heck as to what is what. I hope some good comes from this comment, cheers.
    (6 votes)
    Default Khan Academy avatar avatar for user
    • aqualine seed style avatar for user douglas
      It would be very inconvenient to draw things the same size they are in real life, so they are drawn smaller and the ratio is given.

      1:80 just means that, for every unit in the drawing, there are 80 units in the real thing. Sal still multiplies by 80 because he interpreted the ratio the other way around, he read it as: for every 80 units in the house, there is 1 unit in the drawing. But, conventionally, the first number refers to the scaled version and the second number, to the actual thing.
      (8 votes)
  • duskpin ultimate style avatar for user Abhigyan Basak
    how can we measure the area with the help of scale
    (5 votes)
    Default Khan Academy avatar avatar for user
    • piceratops ultimate style avatar for user Barrett Southworth
      Ok a blueprint example. Lets say 1 inch on the drawing is the same as 2 feet in the real world. So, what's the area of a room that is on the drawing 6 inches by 5 inches. Well convert to the real world area first, so 6 inches = 12 feet and 5 inches = 10 feet. Multiply 12 by 10 and the area of the room is 120 square feet.
      (6 votes)
  • blobby green style avatar for user gaige comeaux
    why is the bisector not parallel to the quadrant's perpendicularity
    (4 votes)
    Default Khan Academy avatar avatar for user
  • mr pants pink style avatar for user cordajia.richardson
    i dont get it at all , can you explain more?
    (4 votes)
    Default Khan Academy avatar avatar for user
  • piceratops seed style avatar for user Lawrence Ualesi
    I dont get the house assumption
    (3 votes)
    Default Khan Academy avatar avatar for user
  • blobby green style avatar for user burtpj07
    Juan classroom shaped like rectangular. Room 40ft long and 25 ft wide. Which could be scale drawing? 5×4cm or 4x2.5 cm or 3x2.5 cm or 4x1 cm
    (4 votes)
    Default Khan Academy avatar avatar for user
  • leaf red style avatar for user markaela.888831501
    why did they make the shape like that.
    (5 votes)
    Default Khan Academy avatar avatar for user

Video transcript

Maya and Mabel are inspecting a 80 to 1 scale floor plan of their new house. The dimensions of the living room in the scaled plan are 4 centimeters by 5 centimeters right over here. What is the area of the living room in the real world? So they gave us these dimensions right over here. This is the scale plan, and then we could figure out these dimensions in the real world by looking at the scale factor right over here. It's an 80 to 1 scale floor plan. And we can assume that the house is much bigger than the floor plan. So the 80, for every 80 units in the house, that represents 1 unit on the floor plan. So if we had 80 meters in the house, that would be represented as 1 meter on the floor plan. If we had 80 centimeters in the house, that would be represented by 1 centimeter in the floor plan. And it goes the other way around. 1 centimeter on the floor plan would represent 80 centimeters in the house. And it's always important to do-- if this confuses you, just always do a reality check that the house should be bigger than the floor plan. So if the floor plan for this dimension of our living room is 4 centimeters, the actual house will be 80 times that. And 80 times 4 is 320-- let me do that in a blue color-- is equal to 320 centimeters. And we can do the same thing for the length of the living room. So 80 times 5 centimeters is going to get us to-- is going to be-- 80 times 5 is 400 centimeters. So we could figure out the area of this room in centimeters, if we like, and I guess, why not? It might be easier to convert it to meters later. So let's see, 400 centimeters times 320 centimeters. Let me write this down. 400 times 320. Let's think about it. 4 times 32 is going to be 120, plus 8, 128. And I have 1, 2, 3 zeroes. 1, 2, 3. So it's going to be 128,000 centimeters squared. Now that's a lot of square centimeters. What would we do if we wanted to convert it into meters? Well, we just have to figure out how many square centimeters are there in a square meter. So let's think about it this way. A meter is equal to-- 1 meter is equal to 100 centimeters. So a square meter, so that's right over there. 1 meter squared would be 1 meter by 1 meter, which is the same thing as 100 centimeters by 100 centimeters. And so if you were to calculate this area in centimeters, 100 times 100 is 10,000, is equal to 10,000 centimeters squared. So you have 10,000 square centimeters for every square meter. And so, if you want to convert 128,000 centimeters squared to meters squared, you would divide by 10,000. So dividing that by 10,000 would give us 12.8 square meters. Now, another way you could've done it, and maybe this would have been easier, is to convert it up here. Instead of saying 400 centimeters times 320 centimeters, you would say, well, 400 centimeters, that's going to be 4 meters. And 320 centimeters, well, that's 3.2 meters. And you would say, OK, 4 times 3.2, that is 12.8 square meters. But either way, the area of the living room in the real world in meters squared, or square meters, is 12.8.