Kitchen science · Fermentation and measurement

Scaling a recipe: ratio, proportion and the scale factor in the kitchen

How do you turn red lentil soup for 4 into soup for 10? Learn to find the scale factor, deal with ingredients you can't split and use glass and spoon measures, and see why cooking time and tin size don't scale in a straight line.

16 min
2 simulations
Mini quiz

Updated: 22 October 2026

Preview

The question

The red lentil soup recipe you have serves 4, but tonight there will be 10 people at the table. Double everything and there won't be enough soup; triple it and there'll be a lot left over. What is the right number?

How many onions does the recipe's "1 onion" become for 10 people? And if the soup becomes 2.5 times bigger, does it take 2.5 times as long to cook?

Try it yourself

No account needed: change the values and check your answer. Some simulations ask for a prediction before they start; it doesn't matter whether it's right or wrong.

Recipe scaler

Red lentil soup for 10

Increase or decrease each ingredient in its own steps. The readout shows each ingredient's factor (new ÷ old) and the amount per person. When you have set them all, press Check.

Predict first

When you scale a recipe for 4 up to 10 people, what should you do to each ingredient?

It doesn’t matter whether you’re right; the simulation opens once you choose.

Number line

A bigger tin, a bigger area

Drag the marker or move it in steps of 0.25 with the arrow keys, then press Check.

Predict first

When the diameter of a round tin becomes 1.5 times bigger, how many times bigger do you think its base area becomes?

It doesn’t matter whether you’re right; the simulation opens once you choose.

Lab

The square-cube law

Open full page in the Lab →

Fig. 1The square-cube law

Change k: the surface grows as k², the weight as k³; watch the stress on the gauge

Gauge (load ÷ strength): 0.1

Scale kk = 1

Leg thickness

Your own values

k (scale)

Safety margin

Safety margin: how many times the load they carry the legs of the k = 1 model can take before breaking (an assumption of the model).

k from 0.1 to 1,000, safety margin 1–1,000. A value applies when you press Enter or leave the box.

Scaled up

The legs hold

Length (k): ×1
Surface (k²): ×1
Volume and weight (k³): ×1
Leg cross-section (k²): ×1
Stress in the legs (k): ×1
Surface ÷ volume (1/k): ×1

Body: 72 unit squares on the surface, 36 unit cubes inside.

Gauge (load ÷ strength): 0.1 · With this rule the legs reach their breaking limit at k = 10.

Leg length ÷ diameter: ×1

Length, surface and volume (logarithmic axes)

length (k)
surface (k²)
volume (k³)

Learn

Progress is kept on this page only; no points are given.

1Predict
2Try
3Explain

If the model is made twice as big in every direction (length, width and height), how many times heavier does it get?

When a body is scaled up k times in every direction without changing its shape, its surface grows k² times and its volume and weight k³ times. Legs carry the weight on their cross-section, and a cross-section is a surface (k²). So the stress grows k³ ÷ k² = k times, and in a big enough model the legs break. The elephant rule is a thought experiment: if the leg diameter grows as k^1.5, the cross-section grows as k³ and the stress stays the same. In real mammals bone diameter grows roughly as M^0.36 (M: body mass); big animals mostly cope with upright posture. Model: one material, an animal standing still, the weight shared equally by four legs; the safety margin is an assumption. Sources: Galileo, Two New Sciences (1638), second day; J. B. S. Haldane, “On Being the Right Size” (1926); A. A. Biewener, Science 245 (1989).

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Frequently asked

5 questions

How do I scale a recipe for 4 people up to 10?

First find the scale factor: the new number of people divided by the number in the recipe, so 10/4 = 2.5. Then multiply every ingredient by that number. For example, 2 tablespoons of butter becomes 2 × 2.5 = 5 tablespoons.

If there are 6 more people, can't I just add 6 to each ingredient?

No, that is thinking in addition. If 1 teaspoon of salt becomes 7 teaspoons, the soup is inedible. The number of people and the amount of each ingredient are directly proportional; proportion works by multiplication, and the ratios between ingredients stay the same.

If the recipe is 2.5 times bigger, does the cooking time go up 2.5 times too?

No. A bigger pot takes longer to come to the boil, but once it boils the lentils need about the same time to soften. Cooking time depends on the amount, the shape of the pot and the size of the pieces; it is not directly proportional to the number of people.

Should I make the cake tin 2.5 times wider too?

No. The base area grows with the square of the diameter: a 2.5 times wider tin has 6.25 times the area, and the cake comes out paper-thin. To spread 2.5 times the batter at the same depth, the diameter only needs to grow about 1.58 times, from 20 cm to about 31.6 cm.

What do I do if the maths says 7.5 eggs?

Crack 7 eggs, beat the eighth in a separate bowl and add about half of it. A medium egg without its shell is roughly 50 g, so half is about 25 g, which you can easily weigh on a kitchen scale.