Molar to percentage concentration converter
This calculator converts molar concentration to percentage or vice versa.

# Beta version#

BETA TEST VERSION OF THIS ITEM
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# Symbolic algebra

ⓘ Hint: This calculator supports symbolic math. You can enter numbers, but also symbols like a, b, pi or even whole math expressions such as (a+b)/2. If you still don't sure how to make your life easier using symbolic algebra check out our another page: Symbolic calculations

# What do you want to calculate today?#

 Choose a scenario that best fits your needs I know percentage concentration (Cp), density (d) and molar mass (M) and want to calculate molar concentration (Cm)I know molar concentration (Cm), density (d) and molar mass (M) and want to calculate percentage concentration (Cp)I know percentage concentration (Cp), density (d) and molar concentration (Cm) and want to calculate molar mass (M)I know molar concentration (Cm), percentage concentration (Cp) and molar mass (M) and want to calculate density (d)

# Calculations data - enter values, that you know here#

 Molar concentration (Cm) mole per cubic decimeter [mol / dm³]milimole per cubic decimeter [mmol / dm³]micromole per cubic decimeter [µmol / dm³]mole per litre [mol / l]milimole per litre [mmol / l]micromole per litre [µmol / l]yottamole per cubic decimeter [Ymol / dm³]zettamole per cubic decimeter [Zmol / dm³]examole per cubic decimeter [Emol / dm³]petamole per cubic decimeter [Pmol / dm³]teramole per cubic decimeter [Tmol / dm³]gigamole per cubic decimeter [Gmol / dm³]megamole per cubic decimeter [Mmol / dm³]kilomole per cubic decimeter [kmol / dm³]hektomole per cubic decimeter [hmol / dm³]mole per cubic decimeter [mol / dm³]decimole per cubic decimeter [dmol / dm³]centimole per cubic decimeter [cmol / dm³]milimole per cubic decimeter [mmol / dm³]micromole per cubic decimeter [µmol / dm³]nanomole per cubic decimeter [nmol / dm³]pikomole per cubic decimeter [pmol / dm³]femtomole per cubic decimeter [fmol / dm³]attomole per cubic decimeter [amol / dm³]zeptomole per cubic decimeter [zmol / dm³]yoctomole per cubic decimeter [ymol / dm³]yottamole per litre [Ymol / l]zettamole per litre [Zmol / l]examole per litre [Emol / l]petamole per litre [Pmol / l]teramole per litre [Tmol / l]gigamole per litre [Gmol / l]megamole per litre [Mmol / l]kilomole per litre [kmol / l]hektomole per litre [hmol / l]mole per litre [mol / l]decimole per litre [dmol / l]centimole per litre [cmol / l]milimole per litre [mmol / l]micromole per litre [µmol / l]nanomole per litre [nmol / l]pikomole per litre [pmol / l]femtomole per litre [fmol / l]attomole per litre [amol / l]zeptomole per litre [zmol / l]yoctomole per litre [ymol / l]mole per cubic yottameter [mol / Ym³]mole per cubic zettameter [mol / Zm³]mole per cubic exameter [mol / Em³]mole per cubic petameter [mol / Pm³]mole per cubic terameter [mol / Tm³]mole per cubic gigameter [mol / Gm³]mole per cubic megameter [mol / Mm³]mole per cubic kilometer [mol / km³]mole per cubic hektometer [mol / hm³]mole per cubic meter [mol / m³]mole per cubic decimeter [mol / dm³]mole per cubic centimeter [mol / cm³]mole per cubic milimeter [mol / mm³]mole per cubic micrometer [mol / µm³]mole per cubic nanometer [mol / nm³]mole per cubic picometer [mol / pm³]mole per cubic femtometer [mol / fm³]mole per cubic attometer [mol / am³]mole per cubic zeptometer [mol / zm³]mole per cubic yoctometer [mol / ym³] => Percentage concentration (Cp) percent [%]permil [‰]basis point (permyriad) [‱]basis point (permyriad) [‱]percentage in point [pip]tick size (US bonds) [tick]tick size plus (US bonds) [tick+]parts per thousand [ppth]parts per million [ppm]parts per hundred million [pphm]parts per billion [ppb]parts per trillion [ppt]parts per quadrillion [ppq]yottauno [YU]zettauno [ZU]exauno [EU]petauno [PU]terauno [TU]gigauno [GU]megauno [MU]kilouno [kU]hektouno [hU]uno [U]deciuno [dU]centiuno [cU]miliuno [mU]microuno [µU]nanouno [nU]pikouno [pU]femtouno [fU]attouno [aU]zeptouno [zU]yoctouno [yU] <= Molar mass (M) gram per mole [g / mol]kilogram per mole [kg / mol]kiloton (gigagram) per mole [Gg / mol]ton (megagram) per mole [Mg / mol]quintal per mole [q / mol]kilonewton per mole [kN / mol]kilogram per mole [kg / mol]hectogram per mole [hg / mol]decagram per mole [dag / mol]gram per mole [g / mol]carat per mole [ct / mol]centigram per mole [cg / mol]milligram per mole [mg / mol]microgram per mole [µg / mol]nanogram per mole [ng / mol]atomic mass unit per mole [u / mol]long ton per mole [ton / mol]short ton per mole [sh tn / mol]long hundredweight per mole [cwt / mol]short hundredweight per mole [sh cwt / mol]stone per mole [st / mol]pound per mole [lb av / mol]ounce per mole [oz av / mol]dram per mole [dr av / mol]grain per mole [gr / mol]pound per mole [lb t / mol]ounce per mole [oz t / mol]dram per mole [dr t / mol]pennyweight per mole [pwt / mol]scruple per mole [s ap / mol]grain per mole [gr / mol]carat per mole [kt / mol]mite per moledoite per mole <= Density (d) kilograms per cubic meter [kg/m³]kilograms per cubic decimeter [kg/dm³]kilograms per cubic centimeter [kg/cm³]kilograms per cubic milimeter [kg/mm³]grams per cubic meter [g/m³]grams per cubic decimeter [g/dm³]grams per cubic centimeter [g/cm³]grams per cubic milimeter [g/mm³]miligrams per cubic meter [mg/m³]miligrams per cubic decimeter [mg/dm³]miligrams per cubic centimeter [mg/cm³]miligrams per cubic milimeter [mg/mm³]exograms per liter [Eg/l]teragrams per liter [Tg/l]gigagrams per liter [Gg/l]megagrams per liter [Mg/l]kilograms per liter [kg/l]hektograms per liter [hg/l]dekagrams per liter [dg/l]grams per liter [g/l]decigrams per liter [dg/l]centigrams per liter [cg/l]miligrams per liter [mg/l]micrograms per liter [µg/l]nanograms per liter [ng/l]picograms per liter [ng/l]femtograms per liter [fg/l]attograms per liter [ag/l]pounds per cubic inch [lb/in³]pounds per cubic foot [lb/ft³]pounds per cubic yard [lb/yd³]pounds per gallon (US) [lb/gal (US)]pounds per gallon (UK) [lb/gal (UK)]ounces per cubic inch [oz/in³]ounces per cubic foot [oz/ft³]ounces per gallon (US) [oz/gal (US)]ounces per gallon (UK) [oz/gal (UK)]grains per gallon (US) [gr/gal (US)]grains per gallon (UK) [gr/gal (UK)]grains per cubic foot [gr/ft³]tons (short) per cubic yard [ton (short) / yd³]tons (long) per cubic yard [ton (long) / yd³]slugs per cubic foot [slug/ft³]psis per 1000 foots [psi/1000ft]earth density (mean) [earth density]water density (0 °C, solid) [water (0 °C)]water density (20 °C) [water (20 °C)]water density (4 °C) [water (4 °C)] <=

# Units normalization#

 Percentage concentration (Cp) Show source$98\ \left[\mathrlap{\it{/}}{^0}_{\,0}\right]$ Density (d) Show source$1840\ \left[\frac{g}{dm^3}\right]$ Molar mass (M) Show source$98.079\ \left[\frac{g}{mol}\right]\ =\ \frac{98079}{1000}\ \left[\frac{g}{mol}\right]$ Molar concentration (Cm)

# Result: Molar concentration (Cm)#

Summary
Used formulaShow source$Cm=\frac{Cp \cdot d}{M \cdot 100}$
ResultShow source$\frac{1803200}{98079}$
Numerical resultShow source$18.38517929424239643552646336116803801017547079395181435373525423\ \left[\frac{mol}{dm^3}\right]$
Result step by step
 1 Show source$\frac{98 \cdot 1840}{\frac{98079}{1000} \cdot 100}$ Removed double fractional mark Divide by fraction is the same as multiply by fraction inverse: $\frac{a}{\frac{c}{b}} = a \cdot \frac{b}{c} = \frac{a \cdot b}{c}$ 2 Show source$\frac{98 \cdot 1840 \cdot 1000}{98079 \cdot 100}$ Simplify arithmetic - 3 Show source$\frac{180320 \cdot 1000}{98079 \cdot 100}$ Simplify arithmetic - 4 Show source$\frac{180320 \cdot 1000}{9807900}$ Simplify arithmetic - 5 Show source$\frac{\cancel{180320000}}{\cancel{9807900}}$ Cancel terms or fractions Dividing a number by itself gives one, colloquially we say that such numbers "cancel-out": $\frac{\cancel{a}}{\cancel{a}} = 1$to find-out the simplest form of fraction we can divide the numerator and denominator by the greatest common divisor (GCD) of both numbers. 6 Show source$\frac{1803200}{98079}$ Result Your expression reduced to the simplest form known to us.
Numerical result step by step
 1 Show source$18.38517929424239643552646336116803801017547079395181435373525423$ The original expression - 2 Show source$18.38517929424239643552646336116803801017547079395181435373525423$ Result Your expression reduced to the simplest form known to us.
Units normalization
Show source$18.38517929424239643552646336116803801017547079395181435373525423\ \left[\frac{mol}{dm^3}\right]$

# Some facts#

• Concentration determines the amount of substance in the mixture. The mixture is often a solution.
• The molar concentration is the amount of moles of substance per volume unit of the solution.
$C_m = \dfrac{n}{V}$
where:
• $C_m$ - molar concentration of solution,
• $n$ - amount of moles of substance,
• $V$ - volume of solution.
• The basic unit of molar concentration is mole per cubic decimeter:
$\dfrac{mol}{dm^3}$
• The percent concentration (weight-based) is the amount of grams of substance per 100 grams of the solution expressed as a percentage.
$C_p = \dfrac{m_s}{m_r} \times 100\%$
where:
• $C_p$ - percentage concentration (weight),
• $m_s$ - mass of substance,
• $m_r$ - mass of solution.
• To convert percentage to molar concentration, we can use the following formula:
$C_m = \dfrac{C_p \times d}{M \times 100}$
where:
• $C_m$ - molar concentration,
• $C_p$ - percentage concentration,
• $d$ - density of solution,
• $M$ - molar mass of substance.
• To convert molar to percentage concentration, we can use the following formula:
$C_p = \dfrac{C_m \times M \times 100}{d}$
where:
• $C_p$ - percentage concentration,
• $C_m$ - molar concentration,
• $d$ - density of solution,
• $M$ - molar mass of substance.

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