# Water Potential Calculator

By Davide Borchia
Last updated: Oct 14, 2021

Water potential controls which direction water in plants and other biological and engineering systems flows: the water potential calculator allows you to compute this value in many different situations.

The water potential explains how trees can grow so high, how plants can absorb water from the soil into their roots and gives us a way to understand how a tree can break through the solid concrete of a sidewalk. Keep on reading to understand how to calculate water potential in plants.

## Measurement units of the water potential

Water potential is measured as energy density (amount of energy per unit of volume or mass).
The units of volumetric energy density are J/m3, which is the same as the pressure unit, Pa.
In some instances, the specific energy (J/Kg) and energy density (J/m3) of a substance are equal to each other, most notably for pure water in standard conditions, where  1 kg = 1 m3. In this water potential calculator, the units used are Pa.

## Water potential components

Many components shape the water potential, but usually only a few of them are relevant in any given problem.

The possible components of the water potential equation are:

• Osmotic potential is the energy required to form an equilibrium between a solution and pure water separated by a semipermeable membrane. It cannot be positive. To learn more, try our osmotic pressure calculator.
• Pressure potential is the hydrostatic pressure exerted on the water. It can be either positive or negative.
• Pneumatic potential is the external pressure on the liquid, either positive or negative.
• Matric potential describes the affinity between the water and the matrix (for example, soil). It must be negative or zero.
• Overburden pressure potential is analogous to the pressure potential but is exerted by the matrix on the water. It is particularly important for deeper soils, where the weight of the overburden is substantial. It can only be positive or zero.
• Gravitational potential defines the effect of the gravitational field on the water. You can calculate it with our potential energy calculator.

## How do I calculate water potential?

Calculating water potential in plants or any other systems with our calculator is pretty simple: just follow the steps, and the solution will stream towards you!

• Choose the water potential components relevant to your problem; to see the least common ones, you have to click advanced mode.
• Insert the corresponding values, leaving the others empty.
• The water potential calculator will return the final value.

## How is water potential calculated?

Water potential is calculated by summing together the various components. Here is the water potential equation:

 Ψ = Σi Ψi = Ψo + Ψp + Ψa + Ψm + Ψo + Ψg

There are many forms of the equation, so we used the most general in the literature, from the book Developments in Soil Science.

The components are computed in different ways:

• Osmotic potential - Ψo = - ν * c * Χ * R * T ,

where:
* ν - Number of ions dissociating from the molecule of solute;
* c - Concentration in mol/kg;
* Χ - Osmotic coefficient;
* R - Gas constant (8.314 m3Pa/K mol); and
* T - Temperature in K.

• Pressure, Hydraulic and Overburden potentials - They are all related to some type of pressure, hence they are calculated in the same way. The formula is  Ψi = Pi/ρw , where:

• Pi - Pressure relative to the ith component (one of the three); and
• ρw - Water density.
• Matric potential - This is related to the capillary flow equation  Ψm = - 2 * σ/ r * ρ2 , where:

• σ - Surface tension at the interface; and
• r - Pore radius.
• Gravitational potential - Defined as it is usually, that is,  Ψg = - g * z , where:

• g - Gravitational acceleration (9.81 m/s^2); and
• z - Difference in height from a reference level.

## A couple of examples of how water potential works

Seeds need to absorb a lot of water, without any help from roots or leaves - they are "just" tiny capsules ready to sprout! The water potential of a dried seed is between -50 MPa and -350 MPa, so it should not be a surprise that seeds are so thirsty!

Being a tree is not easy, even if, from our rushed and mobile perspective, it may look so.
The biggest challenge a tree faces every day is to make sure that water and nutrients reach the leaves of the highest branches, without moving at all.

In essence, answering this question boils down to the creation of a difference in water potential, with the lowest value corresponding to the top of the tree, and the highest to the roots.
Here every little helps - a tree can be almost 116 meters tall!

First, the tree needs to suck in water from the soil surrounding the roots. Here, the osmotic potential is the relevant component; since it is higher in the soil and lower in the root cells (with a value of -0.5 MPa / -1.0 MPa), water flows into the tree. From there on, it is transported using the tree's xylem, which runs from the roots to the leaves.

The water potential gradient is clear - the atmosphere, in dry conditions, has a water potential of -100 MPa (the component relevant here is the pneumatic potential), and inside the trees the value of the pressure potential varies from -1.2 MPa in the xylem to -3.0 MPa in the topmost leaves. The gravitational potential opposes the flow of water by a factor that, in the tallest trees, can reach up to +1 MPa.

At the final interface between the inside of the leaf cells and the atmosphere, the staggering difference in water potential makes the water leave the leaves, accepting carbon dioxide which can be used in the photosynthetic process.

All of this is accomplished by the perfectly engineered system that is a tree, giving an example of how Nature masters the finest and most efficient hydraulic craftmanship over millennia. Trees surround us, and we often take them for granted, but right below the bark they hide marvels that should leave us awestruck. Don't be shy and show your admiration by hugging a tree!

Davide Borchia
Choose the known components!
Osmotic potential (Ψo)
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Pressure potential (Ψp)
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Gravitational potential (Ψg)
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Water Potential
Ψ
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