Enter the three values you know out of the mass of solute m, the molar mass M, the volume of solution V and the molarity c. The one you leave blank is calculated. Choose a unit for each field (different units are converted automatically).
Leave only the field you want to find blank (fill in exactly three). All values must be numbers greater than 0. For the volume, enter the volume of the whole solution after dissolving. The result also shows the moles of solute (mol) and the mass concentration (g/L).
Result
Fill in three of the fields on the left and press "Calculate". The result will appear here.
Table of Contents
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What you can do on this page
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What is this calculation used for?
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How to Use
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Formula
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Symbols and terms
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Good to know before you start
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How to calculate it in Excel
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How to calculate it in Google Sheets
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How to calculate it in Python
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How to write it in LaTeX and other math languages (copy and paste)
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How to have ChatGPT do the calculation
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DataChef Features
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Related Features
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NumberChef Calculators List
What you can do on this page
- Enter any three of the mass of solute \(m\), the molar mass \(M\), the volume of solution \(V\) and the molarity \(c\), and the one you left blank is calculated
- Each field has its own unit (mass: g, mg, kg; volume: L, mL, m³, cm³; molarity: mol/L, mmol/L, μmol/L, mol/m³). Mixed units are converted automatically
- The result always also shows the number of moles of solute (mol) and the mass concentration (g/L)
- Use it directly for lab work and reports, such as "How many grams of salt do I need to make 2 L of 0.5 mol/L salt water?"
- A plain-language explanation of the formulas and copy-and-paste formulas for Excel, Google Sheets and Python are all on this page
Enter the volume of the solution (the whole liquid after dissolving), not the volume of the solvent (such as water). Dissolving a solute changes the volume slightly, so in the lab you dissolve it first and then fill up to the mark in a volumetric flask.
What is this calculation used for?
Making a solution of a set concentration for a lab
"Make 500 mL of 0.1 mol/L salt water" is one of the first calculations you meet in a school or college lab. The mass you need is mass = molarity × molar mass × volume, so \(0.1 \times 58.44 \times 0.5 \approx 2.92\) g. Weigh this out, dissolve it in water and fill a volumetric flask to exactly 500 mL.
Preparing reagents is part of every chemistry experiment, and this formula is its foundation.
Concentrations of IV fluids such as normal saline (medicine)
Normal saline, used in IV drips, is 9 g of salt dissolved in water and made up to 1 L (9 g/L, or 0.9%). As a molarity, that is \(9 \div 58.44 \approx 0.154\) mol/L. This concentration is chosen so that its osmotic pressure is about the same as that of body fluids.
Managing the concentrations of IV fluids and drugs in hospitals is built on calculations like this (actual dosing is decided by doctors and pharmacists).
Comparing the sugar in drinks by the number of molecules (food)
If a juice contains 45 g of glucose (molar mass 180.16 g/mol) per 1 L, its molarity is \(45 \div 180.16 \approx 0.25\) mol/L.
Comparing by grams (mass concentration) makes heavier molecules look like more, but molarity compares how many molecules are dissolved. Sweetness and osmotic pressure depend on the number of molecules, so this view is useful in food design.
Reading mineral and pollutant levels in tap water and rivers (environment and water quality)
Water quality reports often give results in mg/L (a mass concentration), such as "calcium 20 mg/L", and chemists convert these to molarity. For calcium (molar mass 40.08 g/mol), 20 mg/L is \(0.02 \div 40.08 \approx 0.0005\) mol/L, or about 0.5 mmol/L.
Checking against environmental standards and calculating water hardness are built on this conversion.
Managing nutrient solutions for hydroponics (farming and gardening)
In hydroponic growing of tomatoes or strawberries, growers manage the fertilizer concentration as the plants grow. For example, dissolving 10.11 g of potassium nitrate (KNO₃, formula mass 101.1) per 1 L gives exactly \(10.11 \div 101.1 = 0.1\) mol/L.
What matters for nutrients is the number of ions, so research and nutrient solution recipes usually manage concentrations in molarity (mmol/L).
Formula
Formula for molarity (the definition of molarity)
Standard notation
(the usual math form)
\(c\)
\(=\)
\(n\)
\(\div\)
\(V\)
In words
(symbols replaced with words)
③
\(c\): molarity
\(=\)
①
\(n\): moles of solute
\(\div\)
②
\(V\): volume of solution
The formula in words
①
Take the
\(n\): moles of solute (mol)
②
divide it by the
\(V\): volume of solution (L)
③
and you get the
\(c\): molarity (mol/L)
Quick example
The molarity of a solution made by dissolving 0.5 mol of solute in water and making it up to 2 L is
\(c\): molarity
\(=\)
moles (0.5 mol)
\(\div\)
volume (2 L)
\(0.5 \div 2 = 0.25\)
Key idea
Molarity tells you how many moles of solute are dissolved in 1 L of solution. It is the concentration used most in high school chemistry. Because it counts particles (molecules), it connects directly to reaction calculations (how many moles react with how many moles).
The volume you divide by is not the volume of the solvent (water) but the volume of the whole solution after dissolving.
Formula for the number of moles
Standard notation
(the usual math form)
\(n\)
\(=\)
\(m\)
\(\div\)
\(M\)
In words
(symbols replaced with words)
③
\(n\): moles of solute
\(=\)
①
\(m\): mass of solute
\(\div\)
②
\(M\): molar mass
The formula in words
①
Take the
\(m\): mass of solute (g)
②
divide it by the
\(M\): molar mass (g/mol)
③
and you get the
\(n\): moles of solute (mol)
Quick example
The number of moles in 90 g of water (molar mass of water 18 g/mol) is
\(n\): moles
\(=\)
mass (90 g)
\(\div\)
molar mass (18 g/mol)
\(90 \div 18 = 5\)
Key idea
The number of moles counts particles in bundles of about 6.02×10²³ (Avogadro's number). The mass of 1 mol is exactly the molecular weight with "g" attached (this is the molar mass), so you can turn a mass you measure on a scale into a count of particles.
It is the same idea as counting eggs by the dozen (1 dozen = 12), and the units fit neatly: g ÷ (g/mol) = mol.
Formula for molarity from mass (the formula this calculator uses)
Standard notation
(the usual math form)
\(c\)
\(=\)
\(m\)
\(\div\)
\(M\)
\(\div\)
\(V\)
In words
(symbols replaced with words)
④
\(c\): molarity
\(=\)
①
\(m\): mass of solute
\(\div\)
②
\(M\): molar mass
\(\div\)
③
\(V\): volume of solution
The formula in words
①
Take the
\(m\): mass of solute (g)
②
divide it by the
\(M\): molar mass (g/mol)
to turn it into moles
③
divide again by the
\(V\): volume of solution (L)
④
and you get the
\(c\): molarity (mol/L)
Quick example
The molarity of salt water made by dissolving 100 g of table salt (NaCl, molar mass 58.44 g/mol) in water and making it up to 2 L is
\(c\): molarity
\(=\)
mass (100 g)
\(\div\)
molar mass (58.44 g/mol)
\(\div\)
volume (2 L)
\(100 \div 58.44 \approx 1.711\)
\(1.711 \div 2 \approx 0.856\)
Key idea
This is formula 1 (\(c = n \div V\)) with formula 2 (\(n = m \div M\)) substituted for \(n\). Written as a fraction, it is \(c = \dfrac{m}{M \times V}\). This calculator links the four quantities (\(m\), \(M\), \(V\) and \(c\)) with this formula and finds any one of them from the other three.
Note that dividing the mass by the volume alone, \(m \div V\), gives a different concentration, the mass concentration (g/L). This calculator shows it for reference.
Formula for mass
Standard notation
(the usual math form)
\(m\)
\(=\)
\(c\)
\(\times\)
\(M\)
\(\times\)
\(V\)
In words
(symbols replaced with words)
④
\(m\): mass of solute
\(=\)
①
\(c\): molarity
\(\times\)
②
\(M\): molar mass
\(\times\)
③
\(V\): volume of solution
The formula in words
①
Take the
\(c\): molarity (mol/L)
②
multiply it by the
\(M\): molar mass (g/mol)
③
and by the
\(V\): volume of solution (L)
④
and you get the
\(m\): mass of solute (g)
Quick example
The mass of salt needed to make 2 L of 0.5 mol/L salt water (NaCl, molar mass 58.44 g/mol) is
\(m\): mass
\(=\)
molarity (0.5 mol/L)
\(\times\)
molar mass (58.44 g/mol)
\(\times\)
volume (2 L)
\(0.5 \times 58.44 \times 2 = 58.44\)
Key idea
This formula answers "How many grams of solute should I weigh out to make a solution of a given concentration?", the most common question when preparing a lab. First \(c \times V\) gives the moles you need, \(n\) (mol), and multiplying by the molar mass \(M\) turns that into a mass.
Formula for volume
Standard notation
(the usual math form)
\(V\)
\(=\)
\(m\)
\(\div\)
\(M\)
\(\div\)
\(c\)
In words
(symbols replaced with words)
④
\(V\): volume of solution
\(=\)
①
\(m\): mass of solute
\(\div\)
②
\(M\): molar mass
\(\div\)
③
\(c\): molarity
The formula in words
①
Take the
\(m\): mass of solute (g)
②
divide it by the
\(M\): molar mass (g/mol)
to turn it into moles
③
divide again by the
\(c\): molarity (mol/L)
④
and you get the
\(V\): volume of solution (L)
Quick example
The volume of 0.5 mol/L salt water you can make from 100 g of table salt (NaCl, molar mass 58.44 g/mol) is
\(V\): volume
\(=\)
mass (100 g)
\(\div\)
molar mass (58.44 g/mol)
\(\div\)
molarity (0.5 mol/L)
\(100 \div 58.44 \approx 1.711\)
\(1.711 \div 0.5 \approx 3.42\)
Key idea
This formula answers "If I use all the solute I have and dilute it to the target concentration, how many liters will I get?" It turns the mass into moles \(n\) (mol) by dividing by the molar mass, then finds the volume with \(V = n \div c\) (formula 1 rearranged).
Formula for molar mass (molecular weight)
Standard notation
(the usual math form)
\(M\)
\(=\)
\(m\)
\(\div\)
\(c\)
\(\div\)
\(V\)
In words
(symbols replaced with words)
④
\(M\): molar mass
\(=\)
①
\(m\): mass of solute
\(\div\)
②
\(c\): molarity
\(\div\)
③
\(V\): volume of solution
The formula in words
①
Take the
\(m\): mass of solute (g)
②
and divide it by the product of the
\(c\): molarity (mol/L)
③
and the
\(V\): volume of solution (L)
(this product is the number of moles)
④
and you get the
\(M\): molar mass (g/mol)
Quick example
100 g of a solute was dissolved in water and made up to 2 L, giving 0.5 mol/L. The molar mass of this solute is
\(M\): molar mass
\(=\)
mass (100 g)
\(\div\)
molarity (0.5 mol/L)
\(\div\)
volume (2 L)
\(0.5 \times 2 = 1\)
\(100 \div 1 = 100\)
Key idea
Since \(c \times V\) is the number of moles of solute \(n\) (mol), this formula calculates "mass ÷ moles = mass per 1 mol". It leads to a key idea in chemical analysis: estimating the molar mass (molecular weight) of an unknown substance from measured concentration and volume.
Molarity is the number of moles per 1 L of solution. One formula, \(c = m \div (M \times V)\), links mass, molar mass, volume and molarity. The first step is always to turn the mass into moles by dividing by the molar mass.
Symbols and terms
Symbols
| \(c\) | see | Molarity: the moles of solute per 1 L of solution. It comes from the first letter of "concentration". (Example - for 0.5 mol/L salt water, \(c = 0.5\) mol/L) |
| \(n\) | en | The number of moles. It counts particles (molecules, ions and so on) with Avogadro's number (about 6.02×10²³) as 1 mol. The unit is mol (mole). |
| \(m\) | lowercase em | The mass of solute, the amount of what you dissolve as measured on a scale. It comes from the first letter of "mass". The unit is g or similar. |
| \(M\) | capital em | The molar mass: the mass of 1 mol of the substance (g/mol). It is the same number as the molecular weight (formula mass). (Example - water is 18.02 g/mol.) Be careful not to mix it up with the lowercase \(m\) (mass). |
| \(V\) | vee | The volume of solution, the volume of the whole liquid after dissolving. It comes from the first letter of "volume". The unit is L, mL or similar. |
| mol/L | moles per liter | The unit of molarity: how many moles are dissolved in 1 L of solution. It is often written with the symbol M, as in "1 M" or "0.5 M", read "molar". This M is not the same as the molar mass symbol \(M\), so be careful. |
| g/mol | grams per mole | The unit of molar mass - how many grams there are in 1 mol. |
| g/L | grams per liter | The unit of mass concentration - how many grams are dissolved in 1 L of solution. This calculator shows it for reference. |
Terms
| mole (mol) | The unit for counting particles. Just as 12 eggs make "1 dozen", about 6.02×10²³ particles (molecules, ions and so on) make "1 mol". Atoms and molecules are far too small to count one by one, but counting them in this huge bundle connects them to grams you can weigh on a scale. |
| number of moles (amount of substance) | An amount measured in mol, based on the count of particles. It is a different quantity from mass (g). Chemical reactions happen between particles, so reaction calculations are basically done in moles, not in grams. Its official SI name is "amount of substance". |
| Avogadro's number (Avogadro constant) | The number of particles in 1 mol, about 6.02×10²³. Precisely, it is defined as the Avogadro constant, 6.02214076×10²³ /mol. |
| molecular weight | How many times heavier one molecule is than 1/12 of a carbon-12 atom (no unit). It is the sum of the atomic weights of the atoms in the molecule; for water (H₂O), 1.008×2 + 16.00 ≈ 18.02. For substances that do not form molecules, such as table salt (NaCl), the same sum is called the formula mass. |
| formula mass | The sum of the atomic weights in the chemical formula of a substance made of ions, such as table salt (NaCl). It is used the same way as the molecular weight (NaCl is 22.99 + 35.45 ≈ 58.44). You can enter a formula mass in the molar mass field on this page. |
| molar mass | The mass of 1 mol of a substance (g/mol). It is the molecular weight (formula mass) with the unit g/mol attached, as in "the molecular weight of water is 18.02 → the molar mass of water is 18.02 g/mol → 1 mol of water is 18.02 g". |
| molarity | A concentration given as moles of solute per 1 L of solution (mol/L). Also called molar concentration. It is the standard concentration in high school chemistry, and its strength is that it connects directly to reaction calculations. |
| mass concentration | A concentration given as grams of solute per 1 L of solution (g/L). It equals the molarity × the molar mass. Food labels and water quality reports often use a related unit, mg/L (≈ ppm). |
| solute | The substance that is dissolved. In salt water, it is the salt. It dissolves in the solvent (water) to make the solution (salt water). |
| solvent | The liquid that does the dissolving. In salt water, it is the water. It dissolves the solute (salt) to make the solution (salt water). |
| solution | The whole mixture of solute + solvent. In salt water, it is the salt water itself. For molarity, you use the volume of the solution. |
| mass percent | A concentration given as the mass of solute as a percentage of the mass of the solution (%). Also called percent by mass. Converting it to molarity needs the density of the solution, so this calculator does not cover it. |
Good to know before you start
Here is what helps you use the calculation on this page with real understanding, not just by pressing the button.
| Unit rates (Grade 6) |
|
| Multiplying and dividing decimals (Grades 5–6) |
|
| Solutions and concentration (middle school science) |
|
| Atoms, molecules and chemical formulas (middle school science) |
|
| Moles and molar mass (high school chemistry) |
|
How to calculate it in Excel
Copy the whole table below and paste it into cell A1 in Excel. It works as is.
Table to find the molarity (from moles and volume)
| Moles of solute n (mol) | 0.5 |
| Volume of solution V (L) | 2 |
| Molarity c (mol/L) | =B1/B2 |
Table to find the number of moles
| Mass of solute m (g) | 90 |
| Molar mass M (g/mol) | 18 |
| Moles n (mol) | =B1/B2 |
Table to find the molarity (from mass)
| Mass of solute m (g) | 100 |
| Molar mass M (g/mol) | 58.44 |
| Volume of solution V (L) | 2 |
| Molarity c (mol/L) | =B1/(B2*B3) |
Table to find the mass
| Molarity c (mol/L) | 0.5 |
| Molar mass M (g/mol) | 58.44 |
| Volume of solution V (L) | 2 |
| Mass of solute m (g) | =B1*B2*B3 |
Table to find the volume
| Mass of solute m (g) | 100 |
| Molar mass M (g/mol) | 58.44 |
| Molarity c (mol/L) | 0.5 |
| Volume of solution V (L) | =B1/(B2*B3) |
Table to find the molar mass
| Mass of solute m (g) | 100 |
| Molarity c (mol/L) | 0.5 |
| Volume of solution V (L) | 2 |
| Molar mass M (g/mol) | =B1/(B2*B3) |
After pasting, every row except the last (B1–B2 or B1–B3) is an input, and the last row is calculated automatically.
"=B1/(B2*B3)" means "divide B1 by the product of B2 and B3" ("*" is multiplication and "/" is division).
For example, the first table shows 0.25 (mol/L) in B3, the second 5 (mol) in B3, the third about 0.856 (mol/L) in B4, the fourth 58.44 (g) in B4, the fifth about 3.42 (L) in B4 and the sixth 100 (g/mol) in B4. Just replace the inputs with your own numbers. Enter the values in g, g/mol and L (convert values measured in mg or mL first, using 1 g = 1,000 mg and 1 L = 1,000 mL).
"=B1/(B2*B3)" means "divide B1 by the product of B2 and B3" ("*" is multiplication and "/" is division).
For example, the first table shows 0.25 (mol/L) in B3, the second 5 (mol) in B3, the third about 0.856 (mol/L) in B4, the fourth 58.44 (g) in B4, the fifth about 3.42 (L) in B4 and the sixth 100 (g/mol) in B4. Just replace the inputs with your own numbers. Enter the values in g, g/mol and L (convert values measured in mg or mL first, using 1 g = 1,000 mg and 1 L = 1,000 mL).
How to calculate it in Google Sheets
Copy the whole table below and paste it into cell A1 in Google Sheets. It works as is.
Table to find the molarity (from moles and volume)
| Moles of solute n (mol) | 0.5 |
| Volume of solution V (L) | 2 |
| Molarity c (mol/L) | =B1/B2 |
Table to find the number of moles
| Mass of solute m (g) | 90 |
| Molar mass M (g/mol) | 18 |
| Moles n (mol) | =B1/B2 |
Table to find the molarity (from mass)
| Mass of solute m (g) | 100 |
| Molar mass M (g/mol) | 58.44 |
| Volume of solution V (L) | 2 |
| Molarity c (mol/L) | =B1/(B2*B3) |
Table to find the mass
| Molarity c (mol/L) | 0.5 |
| Molar mass M (g/mol) | 58.44 |
| Volume of solution V (L) | 2 |
| Mass of solute m (g) | =B1*B2*B3 |
Table to find the volume
| Mass of solute m (g) | 100 |
| Molar mass M (g/mol) | 58.44 |
| Molarity c (mol/L) | 0.5 |
| Volume of solution V (L) | =B1/(B2*B3) |
Table to find the molar mass
| Mass of solute m (g) | 100 |
| Molarity c (mol/L) | 0.5 |
| Volume of solution V (L) | 2 |
| Molar mass M (g/mol) | =B1/(B2*B3) |
The same formulas as in Excel work as is. Copy the whole table, paste it into cell A1, and replace the inputs (B1–B2 or B1–B3) with your own numbers.
How to calculate it in Python
mass = 100.0 # mass of solute m (g)
molar_mass = 58.44 # molar mass M (g/mol), the value for table salt NaCl
volume = 2.0 # volume of solution V (L)
moles = mass / molar_mass # moles n = m ÷ M (mol)
molarity = moles / volume # molarity c = n ÷ V (mol/L)
mass_concentration = mass / volume # mass concentration = m ÷ V (g/L)
print(f"Moles: {moles} mol")
print(f"Molarity: {molarity} mol/L")
print(f"Mass concentration: {mass_concentration} g/L")
# Check by working backward: mass m = c × M × V, volume V = m ÷ (M × c)
mass_check = molarity * molar_mass * volume
volume_check = mass / (molar_mass * molarity)
print(f"Check (mass): {mass_check} g")
print(f"Check (volume): {volume_check} L")
Runs with the standard library only. In this example the number of moles is about 1.711 mol, the molarity about 0.8556 mol/L, the mass concentration 50.0 g/L, and the checks give a mass of 100.0 and a volume of 2.0. Change the mass, molar mass and volume at the top and run it again. Enter the values in g, g/mol and L.
How to write it in LaTeX and other math languages (copy and paste)
Formula for molarity (the definition of molarity)
c = n ÷ V
c = \dfrac{n}{V}
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>c</mi>
<mo>=</mo>
<mfrac><mi>n</mi><mi>V</mi></mfrac>
</mrow>
</math>
c = n/V
n/V
c := n/V;
c = n/V;
c = n/V
Formula for the number of moles
n = m ÷ M
n = \dfrac{m}{M}
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>n</mi>
<mo>=</mo>
<mfrac><mi>m</mi><mi>M</mi></mfrac>
</mrow>
</math>
n = m/M
m/M
n := m/M;
n = m/M;
n = m/M
Formula for molarity from mass (the formula this calculator uses)
c = m ÷ (M × V)
c = \dfrac{m}{M V}
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>c</mi>
<mo>=</mo>
<mfrac>
<mi>m</mi>
<mrow><mi>M</mi><mo>⁢</mo><mi>V</mi></mrow>
</mfrac>
</mrow>
</math>
c = m/(M V)
m/(M*V)
c := m/(M*V);
c = m/(M*V);
c = m/(M V)
Formula for mass
m = c × M × V
m = c M V
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>m</mi>
<mo>=</mo>
<mi>c</mi>
<mo>⁢</mo>
<mi>M</mi>
<mo>⁢</mo>
<mi>V</mi>
</mrow>
</math>
m = c M V
c*M*V
m := c*M*V;
m = c*M*V;
m = cMV
Formula for volume
V = m ÷ (M × c)
V = \dfrac{m}{M c}
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>V</mi>
<mo>=</mo>
<mfrac>
<mi>m</mi>
<mrow><mi>M</mi><mo>⁢</mo><mi>c</mi></mrow>
</mfrac>
</mrow>
</math>
V = m/(M c)
m/(M*c)
V := m/(M*c);
V = m/(M*c);
V = m/(Mc)
Formula for molar mass (molecular weight)
M = m ÷ (c × V)
M = \dfrac{m}{c V}
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>M</mi>
<mo>=</mo>
<mfrac>
<mi>m</mi>
<mrow><mi>c</mi><mo>⁢</mo><mi>V</mi></mrow>
</mfrac>
</mrow>
</math>
M = m/(c V)
m/(c*V)
M := m/(c*V);
M = m/(c*V);
M = m/(cV)
How to have ChatGPT do the calculation
You are a molarity calculation assistant. Do the following calculation by actually running Python code, and base your answer only on the numbers from the execution result (do not answer by mental math or guessing). 100 g of table salt (NaCl, molar mass 58.44 g/mol) was dissolved in water and made up to exactly 2 L. Using the molarity formula c = m ÷ (M × V), find each of the following: 1. The molarity of this salt water (mol/L) 2. The number of moles of dissolved salt (mol) 3. The mass of the same salt (g) needed to make 2 L of 0.5 mol/L salt water Show the formulas you used and the numbers from the execution result.
How to Use
-
1Enter your numbersType the numbers you want to calculate with into the input fields
-
2CalculatePress the "Calculate" button
-
3Check the resultThe result appears on the spot. The same page also explains the idea behind the calculation and the formula
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Related Features
Density Calculator (Density, Mass and Volume)
Find density, mass or volume from the other two. It uses the same "amount per unit" idea as molarity
Half-Life Calculator (Initial Amount, Remaining Amount, Time, Half-Life)
Find the initial amount, remaining amount, elapsed time or half-life of a radioactive substance. For decay problems in chemistry and physics
Molar Mass Calculator (Molecular Weight)
Just type a chemical formula to get its molar mass (g/mol). Use it when you need the molar mass for a molarity calculation
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