Lesson 7: What’s the difference between density and unit weight?
How heavy is soil? · about 30 minutesYou will learn
How heavy is soil?
Every foundation, wall and slope is designed against the weight of the ground. Engineers describe how heavy a soil is in two closely related ways: density and unit weight. They are easy to mix up, and mixing them up is one of the most common mistakes in soil calculations. This lesson makes the difference clear.
- Explain the difference between density and unit weight, and when each is used.
- Convert between them confidently, with the right units.
The idea, in plain words
Density: mass in a volume
Density tells you how much mass is packed into each unit of volume:
You will see density in kg/m³ and in Mg/m³ (megagrams per cubic metre). They are easy to convert:
A useful reference: water has a density of 1000 kg/m³ (1.0 Mg/m³). Most natural mineral soils in the ground are roughly 1600 to 2200 kg/m³. Dry, loose sands can be a little lower, and peat and organic soils much lower, down to around 1000 kg/m³.
The idea, in plain words
Unit weight: weight in a volume
Unit weight tells you how much weight, which is a force, sits in each unit of volume:
Density is what you measure
In the lab or on site you weigh a known volume of soil on a balance, which gives a mass in kilograms.
Unit weight is what you design with
Foundations, walls and slopes are about forces. For example, the vertical stress at the base of a uniform layer, from its own weight, is its unit weight times its thickness.
The link
γ = ρ g
Weight is mass pulled down by gravity: W = M × g, where g = 9.81 m/s². Put that into the unit weight equation:
Follow the units through: kg/m³ × m/s² gives N/m³. Engineers work in kN/m³, so divide by 1000.
| If density is in… | To get γ in kN/m³ | Example |
|---|---|---|
| kg/m³ | × 9.81, then ÷ 1000 | 1900 kg/m³ → 18.64 kN/m³ |
| Mg/m³ (or g/cm³) | × 9.81, and that is all | 1.90 Mg/m³ → 18.64 kN/m³ |
Water: the numbers to remember
ρw = 1000 kg/m³ = 1.0 Mg/m³ and γw = 9.81 kN/m³
Avoiding mistakes
Three mistakes to watch for
- Forgetting to divide by 1000. A unit weight of 18 640 kN/m³ is not a soil, it is a slip. Mineral soils are about 16 to 22 kN/m³.
- Mixing cm³ and m³. Lab samples are often measured in cm³. Remember 1 cm³ = 10−6 m³, and 1 litre = 0.001 m³.
- Calling unit weight “density”. They are different quantities with different units. Say which one you mean.
A quick sense check saves embarrassment
Before any number goes into a design, I ask: is it in the right range? Density around 2000 kg/m³ or 2 Mg/m³, unit weight around 20 kN/m³. A value ten or a thousand times off almost always means a units slip somewhere, and it is far easier to catch at your desk than after the design is built on it.
Wherever you are
Most of the world works in kg/m³ and kN/m³. Where imperial units are still used, you may meet unit weights in pounds per cubic foot (pcf); a typical soil of about 120 pcf is roughly 19 kN/m³. Convert everything to one system before you calculate.
Worked example 1
A core-cutter sample
A steel cylinder, 100 mm in diameter and 130 mm long, is pushed into the ground and comes out full of soil. The soil has a mass of 1.95 kg. Find its density and unit weight.
Worked example 2
How much does a lorry load weigh?
A lorry carries 8 m³ of excavated soil with a density of 1.85 Mg/m³. What does the soil weigh in kN?
Route A: through mass
M = 1850 × 8 = 14 800 kg
W = 14 800 × 9.81 = 145 188 N
= 145.2 kN
Route B: through unit weight
γ = 1.85 × 9.81 = 18.15 kN/m³
W = 18.15 × 8
= 145.2 kN
Both routes give the same answer. Use whichever feels more natural, and use the other to check.
Your turn
Four short problems
Task (10 minutes)
- A lab sample has a mass of 0.85 kg and a volume of 450 cm³. Find its density and unit weight.
- A soil has a unit weight of 20.0 kN/m³. What is its density?
- What is the weight, in kN, of 2.5 m³ of soil with a density of 1750 kg/m³?
- A report gives the unit weight of a clay as 1.9 kN/m³. What has probably gone wrong?
Show the answers
1. V = 450 × 10−6 = 4.5 × 10−4 m³. ρ = 0.85 ÷ 4.5 × 10−4 = 1889 kg/m³. γ = 1889 × 9.81 ÷ 1000 = 18.5 kN/m³.
2. ρ = γ ÷ g = 20 000 ÷ 9.81 = 2039 kg/m³ (about 2.04 Mg/m³).
3. M = 1750 × 2.5 = 4375 kg. W = 4375 × 9.81 = 42 919 N = 42.9 kN.
4. It is about ten times too small. Someone has probably written a density of 1.9 Mg/m³ as a unit weight without multiplying by g. The unit weight should be 1.9 × 9.81 = 18.6 kN/m³.
Quick check
Five quick questions
Choose an answer to see the explanation.
Key points
What to take away
- Density ρ = M ÷ V, in kg/m³ or Mg/m³. Unit weight γ = W ÷ V, in kN/m³.
- They are linked by γ = ρ g, with g = 9.81 m/s².
- Shortcut: density in Mg/m³ × 9.81 = unit weight in kN/m³.
- Water: 1000 kg/m³ and 9.81 kN/m³.
- Sense check: most mineral soils are about 1600 to 2200 kg/m³, or 16 to 22 kN/m³.
Up next: Lesson 8
Bulk, dry, saturated or submerged: which density should you use? The same soil has four different densities depending on the water in it. You will learn what each one is and when to use it.
Assessment (optional)
Test yourself properly
Unlike the practice questions, this assessment has no answers on the page. Attempt it on your own, as if it were an exam.
Instructions
- Total: 40 marks. Suggested time: 60 minutes.
- Answer all questions. The marks for each question are shown in brackets.
- You may refer to the lesson notes, but write your answers in your own words.
- Show your working in calculations. Where a question asks you to justify or explain, marks go to your reasoning, not just the final answer.
Section A: Concepts (12 marks)
- Define density and unit weight, and give the usual units of each. [3 marks]
- Write the relationship between unit weight and density, and explain what g is. [2 marks]
- Convert a density of 1.85 Mg/m³ to kg/m³ and to kN/m³. [2 marks]
- Explain why engineers need unit weight, and not just density, when they work out loads and stresses. [2 marks]
- A report gives the unit weight of a clay as 185 kN/m³. What has probably gone wrong, and what is the likely correct value? [3 marks]
Section B: Calculations (16 marks)
A core cutter has an inside diameter of 100 mm and a height of 130 mm. Empty, it weighs 1240 g. Full of soil, it weighs 3250 g.
(a) Calculate the volume of the cutter in m³. [3 marks]
(b) Calculate the mass of the soil. [1 mark]
(c) Calculate the density of the soil in kg/m³. [2 marks]
(d) Calculate its unit weight in kN/m³. [2 marks]
- A lorry carries 12 m³ of soil with a density of 1.9 Mg/m³. Calculate the mass of the load in tonnes and its weight in kN. [3 marks]
- Convert a unit weight of 20.0 kN/m³ to a density in kg/m³. [2 marks]
- A block of soil 2 m long, 3 m wide and 0.5 m deep has a unit weight of 17.5 kN/m³. Calculate its weight. [3 marks]
Section C: Applied case (12 marks)
A colleague’s calculation for a pad foundation excavation, 2 m × 2 m in plan and 1.5 m deep, reads:
Soil density = 1.95. Unit weight = 1.95 × 10 = 19.5. Weight of soil removed = 1.95 × 6 = 11.7 kN.
Write a short technical note to your colleague (maximum 300 words) that:
- identifies every error or missing piece of information in the calculation [4 marks]
- explains the effect of using g = 10 instead of 9.81, and when that may be acceptable [2 marks]
- gives the corrected unit weight and weight of soil removed [3 marks]
- includes a sense check of the corrected values [1 mark]
Clear, well-organised communication. [2 marks]
How your work is judged
| Criterion | What a strong answer shows |
|---|---|
| Technical accuracy | Correct terms, methods and calculations |
| Use of evidence | Conclusions backed by specific information in the question (test results, descriptions, site details) |
| Engineering judgement | Results linked to what they mean for design and construction |
| Communication | Clear, concise and well organised, in your own words |
Want your work marked? (optional)
You’re welcome to complete this assessment for your own practice. If you’d like me to mark it personally and send written feedback within 5 days, you can send it to me for £20. The marking & feedback page explains how.
- Upload one file (PDF, Word or a clear photo of handwritten work) with your name at the top.
- I only mark assessments from this website. I do not mark university or college coursework, assignments or exam answers.
- How your submission and personal details are handled is explained in the privacy policy.
References
- Barnes, G. (2016) Soil Mechanics: Principles and Practice. 4th edn. London: Palgrave.
- British Standards Institution (BSI) (1990) BS 1377-9:1990 Methods of test for soils for civil engineering purposes. In-situ tests. London: BSI.
- British Standards Institution (BSI) (2014) BS EN ISO 17892-2:2014 Geotechnical investigation and testing. Laboratory testing of soil. Determination of bulk density. London: BSI.
- Knappett, J.A. and Craig, R.F. (2019) Craig’s Soil Mechanics. 9th edn. Boca Raton, FL: CRC Press.
Further learning
- See how density is measured: look up demonstrations of the core cutter and sand replacement tests, the two standard field methods.
- Try it at home: fill a measuring jug to the 1-litre mark with dry sand, weigh it, and work out its density in kg/m³ and its unit weight in kN/m³.