A conversion graph is a straight-line graph that shows the relationship between two equivalent quantities — such as miles and kilometres, or pounds sterling and euros. Reading from one axis to the other converts a value from one unit to the other, without needing to remember or apply a formula.
What is a conversion graph and how does it work?
A conversion graph plots one unit on the x-axis and the equivalent values in another unit on the y-axis. Because the relationship between the two units is proportional (or nearly so), the graph is a straight line — often passing through or near the origin.
To use a conversion graph:
- Find your starting value on one axis.
- Draw a vertical line up to the graph (or horizontal line across).
- Read across (or down) to the other axis.
- That reading is your converted value.
The line acts as a look-up table for any value in the range of the graph.
How do you read values from a conversion graph?
Worked example 1: miles to kilometres
A conversion graph shows that 5 miles ≈ 8 kilometres. The x-axis shows miles (0 to 50) and the y-axis shows kilometres (0 to 80).
Reading from the graph:
| Miles | Kilometres (from graph) |
|---|---|
| 10 | 16 |
| 25 | 40 |
| 40 | 64 |
| 50 | 80 |
To convert 30 miles: find 30 on the miles axis, draw a vertical line to the graph, then read across — approximately 48 km.
To convert 56 km back to miles: find 56 on the km axis, draw a horizontal line to the graph, then read down — approximately 35 miles.
How do you draw a conversion graph?
Step 1 — Identify two known equivalent values (a conversion factor).
Step 2 — Plot the origin (0, 0) if the relationship passes through zero (most unit conversions do).
Step 3 — Plot a second point using the conversion factor.
Step 4 — Draw a straight line through both points and extend it to fill the axes.
Step 5 — Label both axes with units and add a title.
Worked example 2: draw a °C to °F conversion graph
The conversion formula is F = 1.8C + 32.
Two useful points:
- C = 0°: F = 32°. Plot (0, 32).
- C = 100°: F = 212°. Plot (100, 212).
Draw a straight line through these two points. Label x-axis "Temperature (°C)" and y-axis "Temperature (°F)".
Notice this graph does not pass through the origin — this is fine. A conversion graph is a straight line but not necessarily proportional (y = mx + c, not just y = mx).
Reading from the graph:
- 20°C → draw up to the line, read across → approximately 68°F
- 77°F → draw across to the line, read down → approximately 25°C
How do you draw a currency conversion graph?
Worked example 3: pounds (£) to euros (€)
Suppose the exchange rate is £1 = €1.18.
Plot: (0, 0) and (100, 118).
Draw a straight line through both points.
| Pounds (£) | Euros (€) — from graph |
|---|---|
| 20 | 23.60 |
| 50 | 59 |
| 80 | 94.40 |
Currency conversion graphs always pass through the origin (£0 = €0) and have a gradient equal to the exchange rate.
What does the gradient of a conversion graph represent?
The gradient = rise ÷ run = (change in y-axis quantity) ÷ (change in x-axis quantity). For a conversion graph, the gradient equals the conversion factor itself. For the miles-to-km graph: gradient = 8/5 = 1.6 km per mile.
If the graph does not pass through the origin (like °C to °F), the gradient is still the rate of change (1.8°F per °C), and the y-intercept represents the offset (32°F when C = 0).
Frequently asked questions
Why do most conversion graphs pass through the origin?
Most unit conversions are proportional: if you double the quantity in one unit, you double the quantity in the other. 0 miles = 0 kilometres; £0 = €0. These relationships always graph as lines through the origin. The exception is temperature (°C to °F), because the zero points on the two scales are different.
How accurate is reading from a graph compared to calculating?
Reading from a graph introduces a small reading error, especially in the middle of the range where the scale may be less precise. For examinations, readings within one or two small squares of the correct answer are usually accepted. For precise conversions, use the formula or a calculator — but for quick everyday estimates, the graph is fast and intuitive.
Can a conversion graph be used for values outside its plotted range?
You can extend the line beyond the plotted range by continuing the straight line, as long as the relationship remains proportional. In exams, stay within the grid provided — extrapolating off the grid is less reliable and often not needed. If you need to convert a value beyond the graph range, use the conversion factor directly (multiply or divide).
How is a conversion graph different from a distance–time graph?
Both are straight-line graphs, but they represent different things. A distance–time graph shows how far something travels over time — the gradient represents speed. A conversion graph shows equivalent amounts in two different units — the gradient represents the conversion rate. The technique for reading values (draw a vertical or horizontal line to the graph) is the same for both.
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