Water Potential Calculator
Work out the water potential of a plant cell or solution from its solute potential and pressure potential, and see which way water will move across the membrane.
🌱 What is Water Potential?
Water potential, written with the Greek letter psi, is a measure of the free energy of water per unit volume, expressed as a pressure in bar or megapascals. Pure water at atmospheric pressure is defined as zero, and anything that reduces the freedom of water molecules pushes the value below zero. Water always moves spontaneously from a region of higher water potential toward a region of lower water potential, which makes this single number the complete predictor of which way water will flow between any two compartments.
In plants it is the quantity that explains the entire journey water takes from soil to atmosphere. Moist soil sits at around -0.1 to -0.3 bar, a root cell perhaps -2 to -5 bar, a leaf mesophyll cell -10 to -15 bar, and the air outside on a dry day at several hundred bar negative. That descending staircase is not a coincidence, it is the gradient that pulls the transpiration stream upward without the plant expending any metabolic energy on the lifting. Agronomists use it to decide irrigation timing, since a crop begins closing stomata once leaf water potential falls past a species-specific threshold. Physiologists use it to interpret plasmolysis experiments, and food scientists use the closely related water activity to predict microbial spoilage.
Two components account for nearly all of it in a cell. Solute potential is the reduction caused by dissolved particles, always negative, and is estimated from the van 't Hoff equation. Pressure potential is the physical pressure term, positive in a turgid cell where the wall pushes back on the protoplast, zero at incipient plasmolysis, and strongly negative in xylem under tension. Gravitational and matric components exist too, but they are usually negligible over the height of a herbaceous plant or inside a laboratory beaker.
The most common mistakes are sign errors and unit mixing. Because the numbers are negative, "higher water potential" means closer to zero, so -2 bar is higher than -8 bar even though 8 is the larger digit. And because one megapascal equals exactly ten bar, an answer can be out by a factor of ten if the two are combined carelessly. This calculator reports both units side by side, applies the correct ionisation constant for the solute you choose, and states plainly which direction water will move against the surroundings you specify.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 — Open Sucrose Solution in Pure Water
0.15 M sucrose (i = 1) at 22 °C, no pressure potential, surrounded by pure water at 0 bar
Example 2 — Turgid Plant Cell
0.3 M sucrose (i = 1) at 25 °C with 5 bar of turgor, in a bathing solution at −3 bar
Example 3 — Dissociating Salt Solution
0.1 M sodium chloride (i = 2) at 20 °C, no pressure potential, surrounded by pure water at 0 bar
❓ Frequently Asked Questions
🔗 Related Calculators
What is the formula for water potential?
Water potential is the sum of solute potential and pressure potential, written as psi = psi_s + psi_p. Solute potential comes from the van 't Hoff equation, psi_s = -iCRT, where i is the ionisation constant, C is molar concentration, R is 0.0831 litre bar per mole per kelvin and T is temperature in kelvin. A 0.15 M sucrose solution at 22 °C gives -3.68 bar.
What is solute potential and why is it negative?
Solute potential, also called osmotic potential, is the reduction in water potential caused by dissolved particles. Solutes lower the free energy of water relative to pure water, which is defined as zero, so the value is always negative or zero. The more particles per litre, the more negative it becomes.
What is the ionisation constant i in the van 't Hoff equation?
It is the number of particles a formula unit produces in solution, sometimes called the van 't Hoff factor. Sucrose and glucose do not dissociate, so i is 1. NaCl and KCl split into two ions, so i is 2. CaCl2, MgCl2 and Na2SO4 give three particles, so i is 3. Real values are slightly lower than the ideal integer because of ion pairing.
Which way does water move between two solutions?
Water always moves from the higher (less negative) water potential toward the lower (more negative) one, down the free-energy gradient. A cell at -3.68 bar placed in pure water at 0 bar takes water in. The same cell placed in a solution at -6 bar loses water and begins to plasmolyse.
What is the difference between water potential in bar and MPa?
They measure the same quantity in different pressure units, and one megapascal equals exactly 10 bar. To convert, divide bar by 10 to get MPa. A solute potential of -7.43 bar is -0.743 MPa. Most modern plant physiology texts use MPa, while older work and many lab handouts use bar.
What is pressure potential in a plant cell?
Pressure potential is the physical pressure component of water potential, which in a turgid plant cell is the outward push of the protoplast against the cell wall, typically 3 to 7 bar. It is positive in turgid cells, zero at incipient plasmolysis, and strongly negative in xylem vessels under transpirational tension.
How does temperature affect water potential?
Solute potential is directly proportional to absolute temperature, so warming a solution makes it slightly more negative. Going from 20 °C to 30 °C raises T from 293.15 K to 303.15 K, a rise of about 3.4 percent, so a -4.87 bar solution becomes about -5.04 bar. The effect is real but far smaller than a change in concentration.
What is the relationship between water potential and osmotic pressure?
They are the same magnitude with opposite sign. Osmotic pressure is iCRT and solute potential is -iCRT, so a solution with an osmotic pressure of 4.87 bar has a solute potential of -4.87 bar. Osmotic pressure describes the pressure needed to stop osmosis, while solute potential describes the tendency of water to leave.
Why is R given as 0.0831 rather than 8.314?
It is the same gas constant in different units. The SI value 8.314 is in joules per mole per kelvin. Dividing by 100 converts to litre bar per mole per kelvin, giving 0.08314, which is rounded to 0.0831 in most plant physiology texts so the answer comes out directly in bar.
What is incipient plasmolysis?
It is the point at which the protoplast has just begun to pull away from the cell wall, so the wall exerts no pressure and pressure potential is exactly zero. At that point total water potential equals solute potential, which is why finding the external concentration causing 50 percent plasmolysis measures a cell's solute potential.
Can water potential ever be positive?
Total water potential can be positive when pressure potential exceeds the magnitude of solute potential, which happens in root pressure and in guttating plants. Solute potential itself is never positive, since adding solute can only reduce the free energy of water relative to the pure liquid.
What units does this calculator use?
Concentration is entered in moles per litre, temperature in degrees Celsius, and both pressure potential and the surrounding water potential in bar. Results are reported in bar with a megapascal conversion, and osmotic pressure is given in bar.