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Pressure in a liquid calculator

GCSEA-level Forces

The pressure caused by a column of liquid depends on its depth, its density and gravitational field strength.

p = h ρ g

This free calculator is for GCSE and A-level physics. Choose the quantity you want to find, enter the other values with their units, and it shows the working in the layout used in exams, with the answer to the number of significant figures you choose. The values shown are an example. Change them to your own.

Quantity to find

1.18 × 105 Pa

Working

  1. Write the equation
    p = h ρ g
  2. Constants used
    g = 9.8 N/kg
  3. Substitute the values
    p = 12 × 1000 × 9.8
  4. Calculate
    p = 1.176 × 105 Pa
  5. Give the answer to 3 significant figures
    p = 1.18 × 105 Pa

Worked example

Find p, the pressure due to the liquid. Given: depth of the liquid h = 12.0 m; density ρ = 1000 kg/m³; gravitational field strength g = 9.8 N/kg.

  1. Write the equation
    p = h ρ g
  2. Constants used
    g = 9.8 N/kg
  3. Substitute the values
    p = 12 × 1000 × 9.8
  4. Calculate
    p = 1.176 × 105 Pa
  5. Give the answer to 3 significant figures
    p = 1.18 × 105 Pa

Symbols and units

SymbolQuantitySI unit
pPressure due to the liquidPa
hDepth of the liquidm
ρDensitykg/m³
gGravitational field strength (constant)N/kg

Pressure in a liquid: rearranged

  • To find pressure due to the liquid: p = h ρ g
  • To find depth of the liquid: h = p / (ρ g)
  • To find density: ρ = p / (h g)

Exam tip

h is the vertical depth below the surface, not the distance along a slope or pipe. Add atmospheric pressure for the total.

Common questions

What is the formula for pressure in a liquid?

The equation is p = h ρ g, where p is the pressure due to the liquid (Pa); h is the depth of the liquid (m); ρ is the density (kg/m³); g is the gravitational field strength (N/kg).

What units should I use for pressure in a liquid?

In SI units: pressure due to the liquid in Pa, depth of the liquid in m, density in kg/m³, gravitational field strength in N/kg. The calculator also accepts common alternatives such as kilometres, grams or minutes, and converts them for you.

How do I rearrange p = h ρ g?

Rearranging gives these forms: to find pressure due to the liquid: p = h ρ g. to find depth of the liquid: h = p / (ρ g). to find density: ρ = p / (h g).

Practise pressure in a liquid questions

Press the button for a question with random numbers. Work it out on paper first, then type your answer.

Related

More forces equations: Newton’s second law, Weight, Moment of a force, Hooke’s law, Pressure, Density, Horizontal component of a force, Vertical component of a force. See the full list on the physics equation calculator page.