Conversion Graphs

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What is a Conversion Graph?

A conversion graph is a straight-line graph used to convert between two units. Because the relationship is proportional (twice the miles = twice the km), the line always passes through the origin (0, 0).

To read the graph: draw a vertical line from the value on one axis up to the line, then a horizontal line across to the other axis.

🔑 Key fact: Conversion graphs are always straight lines through (0, 0). Zero of one unit = zero of the other. The steeper the line, the greater the rate of conversion (larger gradient).

Gradient = rise ÷ run = (change in y-value) ÷ (change in x-value)

Example — Find the gradient of a miles-to-km graph passing through (0, 0) and (5, 8)

Step 1

Pick any point on the line other than the origin — here, (5, 8) means 5 miles corresponds to 8 km.

Step 2

Gradient = rise ÷ run = \(\dfrac{8}{5} = 1.6\)

Step 3 — What it means

The gradient is the conversion rate: 1.6 km for every 1 mile. On a conversion graph, the gradient always equals "how many of the y-axis unit per 1 of the x-axis unit."

📝 Example 1: Draw a miles–km graph, given 5 miles = 8 km

Step 1

Plot (0, 0) — the origin. Zero miles = zero km.

Step 2

Plot (5, 8) using the given conversion fact.

Step 3

Draw a straight line through both points and extend it across the full graph.

Step 4 — Read off values

To convert 10 miles: find 10 on x-axis, draw up to line, read across → 16 km.

✓ Quick Check 1 — Reading Values from Conversion Graphs

Question 1 of 10

Reading Conversion Graphs

You can use a conversion graph to convert in both directions — from one unit to the other, or back again. Always:

Find your starting value on the correct axis
Draw a line parallel to the other axis until you reach the conversion line
Read the value from the second axis

⚠ Important exception: The Celsius to Fahrenheit graph does NOT pass through the origin because 0°C = 32°F (not 0°F). It is still a straight line, but its y-intercept is 32. This is the only common conversion graph that does not pass through (0, 0).

📝 Example 2: Read 25°C in Fahrenheit from the graph

Step 1

Find 25 on the Celsius axis (x-axis).

Step 2

Draw a vertical dotted line up to the conversion line.

Step 3

Draw a horizontal dotted line across to the Fahrenheit axis — read off 77°F.

25°C = 77°F (check: 25 × 9/5 + 32 = 45 + 32 = 77 ✓)

📝 Example 3: Use the currency graph to convert £60 to euros (£1 = €1.15)

From the graph

Find £60 on x-axis, draw up to line, read across → €69.

Check by calculation

£60 × 1.15 = €69 ✓

£60 = €69

✓ Quick Check 2 — Interpreting Scales and Intermediate Values

Question 1 of 10

Interactive Conversion Graph Tool

Select a conversion type, enter a value and click Convert to see the result drawn on the graph with a dotted guideline.

📊 Clickable Conversion Graph

Conversion type

Enter miles

✓ Quick Check 3 — Mixed Graph Reading and Conversion

Question 1 of 10

Practice: Conversion Graphs

Use £1 = €1.15 and F = C × 9/5 + 32. Enter your answers as numbers.

#	Question	Answer	Result
1	Convert £20 to euros
2	Convert €92 to pounds
3	Convert 20°C to Fahrenheit
4	Convert 50°C to Fahrenheit
5	Convert 68°F to Celsius
6	Convert £50 to euros
7	Convert €46 to pounds
8	Convert 100°C to Fahrenheit
9	Convert 0°C to Fahrenheit
10	Convert 32°F to Celsius

⚠ Things to Watch Out For

Read from the correct axis — find your value on one axis first, then go to the line, then across to the other axis.
Don't read the value directly without going to the line first — always use the graph itself to convert.
Read the scale carefully — each small square may represent 2, 5, or another value, not always 1.
Don't assume the graph passes through the origin — check before extrapolating back to zero.
Don't use the graph for values outside the plotted range — you cannot reliably extend beyond the data shown.

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Learning Objectives

Real-World Applications

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Example — Find the gradient of a miles-to-km graph passing through (0, 0) and (5, 8)

📊 Clickable Conversion Graph

Practice: Conversion Graphs

⚠ Things to Watch Out For