Mass Percent Calculator

Concentrated lab reagents: % w/w to molarity

Mass Percent Calculator: Complete Guide

Mass percent (% w/w) is the mass of solute as a percentage of total solution mass: w% = (m_solute / m_solution) x 100, where m_solution = m_solute + m_solvent. This calculator solves all three forms: find percent, find solute mass, find solution mass.

Formula and worked examples

Example 1: dissolve 10 g NaCl in 190 g water. m_solution = 200 g. w% = (10/200) x 100 = 5.0%. Example 2: make 0.9% w/w saline in 1000 g: m_NaCl = 0.9/100 x 1000 = 9 g; m_water = 991 g. Example 3: concentrated HCl is 37% w/w (density 1.19 g/mL). In 1 litre (1190 g): m_HCl = 0.37 x 1190 = 440.3 g; moles = 440.3/36.461 = 12.07; molarity = 12.07 mol/L.

% w/w vs % w/v vs % v/v

Mass percent (% w/w): g solute per 100 g solution -- temperature-independent; used for concentrated reagents, alloys, food composition. Volume percent (% v/v): mL solute per 100 mL solution -- for liquid-liquid mixtures (ethanol in beverages, spirits 40% v/v). Mass-volume percent (% w/v): g solute per 100 mL solution = g/dL -- the default in pharmacy and biology (0.9% w/v saline = 9 g/L). For dilute aqueous solutions at 25 degrees C, % w/w approximately equals % w/v because density is approximately 1 g/mL. For concentrated solutions they differ substantially -- always specify which percent is being used.

Converting % w/w to molarity

Molarity = (% w/w x density x 10) / molar mass. In 1 litre of solution: mass = density (g/mL) x 1000 (mL); mass of solute = mass x % w/w / 100 = density x % w/w x 10; moles = density x % w/w x 10 / molar mass. Reference values at 25 degrees C: 37% HCl (rho 1.19, M_r 36.461) = 12.1 mol/L; 98% H2SO4 (rho 1.84, M_r 98.079) = 18.4 mol/L; 70% HNO3 (rho 1.42, M_r 63.013) = 15.8 mol/L; 28% NH3 aq (rho 0.90, M_r 17.031) = 14.8 mol/L; 30% H2O2 (rho 1.11, M_r 34.015) = 9.8 mol/L. Always add concentrated acids to water, not water to the acid.

Mass percent in food, materials and industry

Nutritional labelling: fruit juice approximately 10% w/w sugar; whole milk 3.5% w/w fat; eggs 12% w/w protein. Alloys: 304 stainless steel 18% w/w Cr + 8% w/w Ni; 18-carat gold 75% w/w Au. Pharmaceutical tablets: a 500 mg API in a 600 mg tablet = 83.3% w/w. Mining: gold ore at 5 g per tonne = 5 x 10^-4% w/w = 5 ppm. Sea water: approximately 3.5% w/w dissolved salts = 35 g/kg = 35 ppt.

Using this calculator in lab and coursework

All calculations run in your browser -- no data is sent to any server. Results copy with one click. The formula is shown for verification and citation. This tool is part of the LazyTools mixtures and solutions suite, covering pH, concentration, dilution, molarity, buffer and solution preparation calculations for A-level, IB, AP Chemistry and undergraduate analytical chemistry.

Key solution chemistry relationships

The equations connecting all solution chemistry: c = n/V (molarity); w% = m_solute/m_solution x 100 (mass percent); C1V1 = C2V2 (dilution and titration); pH = -log[H+]; pH = pKa + log([A-]/[HA]) (Henderson-Hasselbalch); pi = iMRT (osmotic pressure). Mastering these and their interconversions covers the quantitative requirements of solution chemistry from A-level through to graduate-level analytical and pharmaceutical chemistry.

Worked example and common errors

A student needs 500 mL of 0.100 mol/L NaOH from 2.00 mol/L stock. Step 1: moles needed = 0.100 x 0.500 = 0.0500 mol. Step 2: volume of stock = 0.0500 / 2.00 = 25.0 mL. Step 3: pipette 25.0 mL of stock into a 500 mL volumetric flask. Step 4: add approximately 400 mL distilled water, mix. Step 5: make up to the 500 mL mark and invert to mix. Common errors to avoid: (1) Confusing mass of solution with mass of solvent -- they differ by the solute mass. (2) Using wrong molar mass -- always check for water of crystallisation in hydrated salts. (3) Unit mismatch -- all concentrations in a calculation must use the same units. (4) Stoichiometric ratio errors -- H2SO4 requires 2 mol NaOH per mol acid. (5) Assuming density equals 1 g/mL for concentrated solutions -- use supplier data sheets for accurate density values of concentrated reagents.

Connecting this calculation to the wider solution chemistry suite

Solution chemistry calculations are deeply interconnected. Molarity (c = n/V) underpins dilution (C1V1=C2V2), which underpins titration (Ca*Va = Cb*Vb at equivalence). Mass percent connects to molarity via M = (% w/w x density x 10) / molar mass. Buffer pH uses Henderson-Hasselbalch, itself derived from Ka = [H+][A-]/[HA]. Buffer capacity is the derivative of the H-H equation. Each calculator in the LazyTools mixtures suite handles one of these interconnected calculations -- use the related tools section to move between calculations in multi-step problems.

Step-by-step worked numerical example

A student needs 500 mL of 0.100 mol/L NaOH from 2.00 mol/L stock. Step 1: moles needed = 0.100 x 0.500 = 0.0500 mol. Step 2: volume of stock required = 0.0500 / 2.00 = 0.0250 L = 25.0 mL. Step 3: using a pipette, transfer exactly 25.0 mL of 2.00 mol/L NaOH stock into a 500 mL volumetric flask. Step 4: add approximately 400 mL of distilled water and swirl gently until fully dissolved. Step 5: allow the solution to cool to room temperature (dilution of NaOH is slightly exothermic). Step 6: top up carefully to the 500 mL graduation mark with distilled water, using a dropper for the final millilitres. Step 7: stopper the flask and invert ten times to homogenise. Label the flask immediately with: solute, concentration, volume, date prepared, and preparer initials. This systematic approach -- moles first, then volume or mass -- avoids unit errors and produces fully traceable calculations for laboratory records, quality management systems and regulatory submissions.

Common errors in solution chemistry calculations

Five frequently made mistakes: (1) Confusing mass of solution with mass of solvent. The mass of the solution is the total mass including the solute: m_solution = m_solute + m_solvent. This error inflates the denominator in % w/w calculations and underestimates the true percent. (2) Wrong molar mass from hydrated salts. CuSO4.5H2O (M_r 249.69) is not the same as anhydrous CuSO4 (M_r 159.61). Always use the formula as written on the reagent bottle, including all water of crystallisation. (3) Mixing units within a calculation. Concentrations in mmol/L and mol/L cannot be combined directly in C1V1=C2V2; convert to the same unit first. (4) Forgetting stoichiometric ratios. H2SO4 provides two H+ per molecule; H3PO4 provides three; NaOH provides one OH per molecule; Ca(OH)2 provides two. Ignoring this in neutralisation calculations leads to errors by factors of 2 or 3. (5) Assuming density equals 1 g/mL for concentrated solutions. This is only valid for dilute aqueous solutions. Concentrated HCl has density 1.19 g/mL; concentrated H2SO4 1.84 g/mL. Always check the supplier certificate of analysis for exact density and percent composition before calculating dilutions or neutralisations.

Connecting this calculation to the broader solution chemistry toolkit

Every solution chemistry calculation connects to others. Molarity (c = n/V) underpins dilution (C1V1=C2V2), which underpins titration (Ca*Va*na = Cb*Vb*nb at the equivalence point). Mass percent connects to molarity via M = (% w/w x density x 10) / molar mass. Buffer pH uses the Henderson-Hasselbalch equation, itself derived from the Ka expression. Buffer capacity (beta = dn/dpH) is the derivative of the H-H equation with respect to pH. Each calculator in the LazyTools mixtures and solutions suite handles one node in this interconnected network -- use the related tools section at the bottom of this page to move between calculations in multi-step problems, and use the copy button to carry results between tools without transcription errors.

Frequently asked questions