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    Liquid Pressure Calculator (p = hρg)

    GCSE PhysicsAQAEdexcelOCRHigher tier, GCSE Physics only

    Find the pressure due to a column of liquid, the depth or the density using p = h × ρ × g. g is set to 9.8 N/kg.

    Quick answer

    Pressure due to a liquid = height (depth) × density × g. Use metres, kg/m³ and N/kg to get pascals. For example, 5 m down in water: 5 × 1000 × 9.8 = 49,000 Pa.

    By Engr. Mehmood Kakar · Updated

    p = h × ρ × g
    Find:

    Water is about 1000 kg/m³. Use the value in the question.

    Simulation

    Deeper means more pressure

    Choose a liquid and the depth of the hole. Water spurts out harder from deeper holes because the pressure from the liquid above is greater.

    6 m

    Pressure in a liquid depends on depth and density, not on the shape or width of the container.

    Put these numbers in the calculator above

    How to calculate pressure in a liquid

    The deeper you go in a liquid, the more liquid is above you and the greater the pressure. The pressure due to a column of liquid is:

    pressure = height of column × density of liquid × gravitational field strength

    • p is pressure in pascals (Pa)
    • h is the height of liquid above the point (the depth) in metres (m)
    • ρ is the density of the liquid in kg/m³
    • g is gravitational field strength in N/kg

    At the bottom of a 5 m deep pool of water (ρ = 1000 kg/m³), the pressure due to the water is 5 × 1000 × 9.8 = 49,000 Pa.

    The pressure acts in all directions and doesn't depend on the shape of the container, only on depth and density. A denser liquid gives a bigger pressure at the same depth. Pressure differences with depth are what cause upthrust on submerged objects.

    Common mistakes that cost marks

    1. Using the depth from the bottom. h is the height of liquid above the point.
    2. Not converting g/cm³. 1.03 g/cm³ is 1030 kg/m³.
    3. Dividing by only one term. h = p ÷ (ρ × g): divide by both.
    4. Forgetting kPa. 20 kPa is 20,000 Pa.

    Practice questions

    Try each one on paper first, then reveal the worked answer.

    Q1Calculate the pressure due to the water at the bottom of a 5.0 m deep pool. Density of water = 1000 kg/m³; g = 9.8 N/kg.[2 marks]
    1. p = h × ρ × g
    2. p = 5.0 × 1000 × 9.8
    3. p = 49,000 Pa
    Q2A diver is 20 m below the surface of the sea. Density of seawater = 1030 kg/m³; g = 9.8 N/kg. Calculate the pressure due to the water.[2 marks]
    1. p = 20 × 1030 × 9.8
    2. p = 201,880 Pa (202,000 Pa to 3 s.f.)
    Q3The pressure due to the water in a swimming pool is 20 kPa. Density = 1000 kg/m³; g = 9.8 N/kg. Calculate the depth.[3 marks]
    1. Rearrange: h = p ÷ (ρ × g)
    2. Convert: p = 20,000 Pa; ρ × g = 9800
    3. h = 20,000 ÷ 9800
    4. h = 2.04 m

    Endless practice

    A new question every time, marked instantly. Work it out on paper, then type your answer.

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    Frequently asked questions

    What is the equation for pressure in a liquid?

    Pressure = height of column × density × gravitational field strength (p = hρg). Pressure is in Pa, height in m, density in kg/m³ and g in N/kg.

    Why does pressure increase with depth?

    At a greater depth there is a taller column of liquid above, so a greater weight of liquid pushes down on each square metre.

    Is p = hρg Higher tier?

    Yes. In AQA it is GCSE Physics (separate science) only, Higher tier.