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Direct Proportion Calculator

Calculate unknown values using direct proportion. If you know one pair of values (x₁, y₁), find y₂ for any x₂ — using the unitary method with step-by-step working.

If x₁ corresponds to y₁, find y₂ when x = x₂.

y₂ (answer)

28

How it works

  1. Identify the relationship (y = kx)

    y=kxy = kx

    In direct proportion, y is proportional to x — as x increases, y increases at the same rate.

  2. Find the constant of proportionality (k)

    k=y1x1=123=4k = \frac{y_1}{x_1} = \frac{12}{3} = 4

    Divide the known y value by the known x value: k = 12 ÷ 3 = 4.

    Result:k = 4

  3. Calculate the unknown value

    y2=k×x2=4×7=28y_2 = k \times x_2 = 4 \times 7 = 28

    Multiply k by x₂: 4 × 7 = 28.

    Result:28

Direct Proportion

y=kxk=y1x1y2=k×x2y = kx \qquad k = \frac{y_1}{x_1} \qquad y_2 = k \times x_2
kkConstant of proportionality (y ÷ x)
x1,y1x₁, y₁Known pair of values
x2x₂New x value (find the corresponding y)

Example substitution

k=123=4⇒y2=4×7=28k = \frac{12}{3} = 4 \quad \Rightarrow \quad y_2 = 4 \times 7 = 28

If 3 costs £12, then k = 4 (cost per unit). For 7: y = 4 × 7 = £28.

Worked examples

If 5 pencils cost £2, how much do 12 pencils cost?

  1. 1
    Find cost per pencil (k): k = £2 ÷ 5 = £0.40
  2. 2
    Multiply by 12: £0.40 × 12 = £4.80
Answer: 12 pencils cost £4.80

A recipe for 4 people needs 200g of flour. How much for 7 people?

  1. 1
    Find flour per person: 200 ÷ 4 = 50g per person
  2. 2
    Multiply by 7: 50 × 7 = 350g
Answer: 350g of flour

Frequently asked questions

What is direct proportion?+

Two quantities are in direct proportion if increasing one causes the other to increase by the same factor. Written as y ∝ x, or y = kx.

How do you solve direct proportion?+

Use the unitary method: find the value for 1 unit, then multiply by the required amount.

If 5 items cost £35, how much do 8 cost?+

1 item costs £35 ÷ 5 = £7. 8 items cost £7 × 8 = £56.

What is the constant of proportionality?+

In y = kx, k is the constant. It is the rate (e.g., price per item, speed, etc.).

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