Soil Water Potential: Formula and Calculation

Calculate soil water potential by combining its pressure, gravitational, and osmotic components; in the common pressure-head method, multiply pressure head by water’s unit weight. Enter pressure head in metres of water and the calculator returns pressure potential in kilopascals, with the equivalent water head shown as a check.

Formula

The calculator uses the pressure-head relationship:

ψ_p = −ρ_w g h

• ψ_p is pressure potential, in kilopascals (kPa).
• h is pressure head, in metres of water (m).
• ρ_w is water density, approximately 1,000 kilograms per cubic metre (kg/m³).
• g is gravitational acceleration, approximately 9.80665 metres per second squared (m/s²).

Combining the constants gives ψ_p ≈ −9.80665h kPa for a soil-water pressure head expressed in metres. The negative sign uses the usual soil-science convention: water under tension, below atmospheric pressure, has negative pressure potential relative to free water at atmospheric pressure. The calculator treats the entered head as a positive magnitude of suction and applies that convention. This is a pressure-potential calculation, not a complete calculation of total soil water potential.

Worked Example

Using the default pressure head of 1 m:

1. Pressure potential = −9.80665 × 1 = −9.80665 kPa.
2. Rounded to two decimal places, pressure potential = −9.81 kPa.
3. The equivalent water head is 1 m.

Thus, the calculator reports −9.81 kPa and a water-head equivalent of 1.00 m. The minus sign indicates suction under the stated convention; it does not mean that the soil contains a negative amount of water.

What Soil Water Potential Means

Soil water potential describes the energy state of water in soil relative to a reference state, commonly free water at atmospheric pressure and at a specified elevation. It helps explain which way water can move: water tends to move from higher potential (less negative) toward lower potential (more negative), subject to the system and its boundary conditions. Potential is expressed as energy per unit volume, such as pascals, or as energy per unit weight, represented by a water head in metres.

It is not the same as soil moisture content. Moisture content tells how much water is present, by mass or volume. Potential describes how strongly that water is held or what energy state it has. Two soils can contain the same amount of water but have different potentials because pore sizes, texture, structure, and water distribution differ. A coarse soil often drains readily, while fine pores can retain water more strongly; exact relationships depend on the soil and its condition.

Components and Sign Convention

Total soil water potential is commonly represented as a sum of components, although which terms matter depends on the problem and the chosen reference:

• Matric potential arises from water’s interaction with soil surfaces and capillary pores. It is usually negative in unsaturated soil and is often the main component considered when describing soil suction.
• Pressure potential reflects hydrostatic pressure. It can be positive below a water table and negative in unsaturated soil when expressed relative to atmospheric pressure.
• Gravitational potential reflects elevation. It changes with vertical position and can be expressed as a head or as an energy per volume.
• Osmotic potential arises from dissolved solutes. It matters especially when considering water movement across membranes, such as in plant-root contexts; it is generally zero for pure water and negative in solutions relative to pure water.

Terminology varies among fields and instruments. Matric potential may be reported separately from pressure potential, or a measurement may effectively represent a combination. Always check the reference level, sign convention, and component measured before comparing values.

How to Calculate or Measure It

This calculator converts a pressure head into pressure potential. Use a head value in metres; for a head measured in centimetres, divide by 100 first. For a value in feet, multiply by 0.3048 to convert to metres. The corresponding pressure is about 0.433 psi per foot of water, or 9.81 kPa per metre, with the sign determined by whether the pressure is above or below the reference pressure.

In practice, soil-water status is often measured rather than calculated from head. Tensiometers measure soil-water tension over a limited operating range and are commonly used in relatively wet soil. Other instruments, such as porous-matrix sensors, infer potential from an equilibrated material. Laboratory methods can measure water-retention relationships across a broader range. Instruments differ in range, response time, calibration, and the potential component they indicate; a reading should not be treated as total potential unless the method supports that interpretation.

Reading the Result and Common Errors

A result of −9.81 kPa corresponds to a pressure head of 1 m under this formula. A more negative pressure potential represents stronger suction relative to atmospheric pressure. In an unsaturated profile, potential commonly varies with depth and water content, so one reading does not necessarily describe an entire field or pot.

• Do not confuse head with depth. Pressure head is a water-energy equivalent, not automatically the sensor’s distance below the surface. Elevation and reference pressure matter.
• Keep units consistent. The formula’s coefficient is in kPa per metre. Entering centimetres as if they were metres makes the answer 100 times too large.
• Use the right sign. The calculator assumes a positive suction-head magnitude and returns a negative pressure potential. If a source gives signed pressure head, interpret its convention before using it.
• Do not infer water content from potential alone. A soil-specific water-retention curve is needed to relate potential to water content.
• Do not confuse kPa with bars or psi. One bar equals 100 kPa; 1 psi is approximately 6.895 kPa. Convert before comparing readings.

Frequently Asked Questions

What is the formula for soil water potential?
For the pressure-head component, ψ_p = −ρ_wgh. With water properties approximated as above, this is about −9.80665 times the suction head in metres, giving kPa.

Is soil water potential the same as soil moisture?
No. Moisture is the quantity of water in soil; potential describes its energy state or how strongly it is held. Measuring one does not uniquely determine the other without information about the soil.

Why is soil water potential usually negative?
Unsaturated soil water is commonly under tension relative to free water at atmospheric pressure. With that reference and sign convention, its pressure or matric potential is negative. Saturated water under hydrostatic pressure can have a positive pressure component.

Can I calculate total soil water potential with this calculator?
No. It calculates pressure potential from a supplied head. Total potential may also require matric, gravitational, and osmotic terms, plus a clearly defined reference and sign convention.

How do I convert soil water potential from kPa to bars?
Divide the kPa value by 100 to obtain bars. For example, −100 kPa equals −1 bar. Keep the sign when converting.

Related

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in h | Pressure head | m | 1 | 0
out psi | Pressure potential | kPa | -9.80665 * h | 2
out head | Water head equivalent | m | h | 2