Solution Spiking Calculator

Raise an existing sample’s concentration by adding a concentrated stock. Find the spike volume, or the required stock concentration when the spike volume is known.

Add to an existing solution

Raise the concentration of an existing sample by adding a concentrated stock. The calculation includes both the stock's solute and its added volume.

Vₓ = Vₚ × (Mf − Mₚ) / (Mₛ − Mf)
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Use 0 for a sample that initially contains none of the added solute.

Concentration basis: Use molarity (M, mM, µM, nM, pM) or % v/v throughout a calculation. % v/v is the volume of a liquid component per 100 volume units of final solution; it is not % w/v or % w/w. These tools do not convert between concentration categories or percentage bases. Solute must be conserved. Calculated added volumes and mixture concentrations assume additive solution volumes; measure the final volume for precise preparation.

Spiking changes solute amount and total volume

Adding concentrated stock can adjust an assay reagent level or add a known analyte amount to a sample. In analytical chemistry and standard-addition protocols, account for the original analyte and the dilution caused by the spike. This calculator plans a spike for a known starting concentration; it does not estimate an unknown concentration from instrument responses.

M·V + Mₛ·Vₓ = Mf·(V + Vₓ)

  • M: present concentration, labeled Mₚ in the calculator.
  • V: present sample volume, labeled Vₚ.
  • Mₛ: concentration of the added stock.
  • Vₓ: spike volume to add.
  • Mf: desired final concentration.

The left side is the original solute amount plus the spike’s solute amount. The right side uses the larger final volume V + Vₓ. Using only the starting volume would overestimate the final concentration.

Vₓ = V(Mf − M)/(Mₛ − Mf)

For a known spike volume, rearrange to Mₛ = [Mf(V + Vₓ) − M·V]/Vₓ. Both workflows assume additive volumes, complete mixing, and no reaction or solute loss.

Example: spike a 1 mL sample to 150 mM NaCl

For a sample initially containing no NaCl, use M = 0, V = 1 mL, Mₛ = 5 M, and Mf = 0.150 M. Then Vₓ = 1 × 0.150 / (5 − 0.150) = 0.0309278 mL, or about 30.93 µL. The final volume is about 1.03093 mL. A 30 µL spike would fall short because it also increases the volume.

Valid concentration relationships

To raise concentration with a positive spike volume, require Mₛ > Mf > M ≥ 0. The sample and spike volumes must be positive. A stock at the target concentration cannot bring a lower-concentration sample exactly to that target with a finite addition. Use the back-dilution tool to lower concentration.

Molarity inputs may use different molarity units. For % v/v inputs, all concentrations must refer to the same liquid component on a volume/volume basis; the balance is an equivalent component-volume balance, not a mole balance. % w/w and % w/v cannot be mixed with % v/v.