Step 1

Calculation basis

Balance basis

Flow unit

All streams use the same basis and rate unit. Changing flow units automatically converts stream rates. Switching between mass and mole bases does not convert compositions or rates, since molecular weights are not used in this version.

Step 2

Components

Define the same components in every stream. Fractions are entered as percentages and must add to 100% for each known stream.

Step 3

Inlet and outlet streams

Solve for

How the calculation works

Choose one unknown stream to solve its flow and full composition, or select “Check entered streams” to report residuals.

Try an example:

A mixing example is loaded. Select Calculate balance to solve the product stream.

Results

Calculate to display the overall balance, calculated stream, and component-by-component breakdown.

Component balance

Residual = inlet flow − outlet flow. Values close to zero are balanced; a positive residual means more enters than leaves.

Component	Inlet rate	Outlet rate	Residual

Material balance equations

At steady state, with no reaction and no accumulation, material entering a defined boundary must equal material leaving that boundary.

Σ inlet flow = Σ outlet flow

Σ (F_in × z_i,in) = Σ (F_out × z_i,out)

Here F is the mass or molar flow rate and z_i is the mass or mole fraction of component i. Each component is conserved separately in this nonreactive model.

All streams use the selected flow unit. Changing flow units converts the rates; switching between mass and mole basis requires new compositions and flows because molecular weights are not supplied.

Worked mixing example

Mix 1,000 lb/h of 90 wt% water with 500 lb/h of 20 wt% water. The outlet is 1,500 lb/h with 1,000 lb/h water (66.67 wt%) and 500 lb/h ethanol (33.33 wt%).

When to use this calculator

Mixing streams of known flow and composition.
Calculating an unknown product or reject stream around a nonreactive separator.
Checking mass or mole closure across a steady-state process boundary.
Estimating stream flow and composition from known surrounding streams.

Limitations and common mistakes

No reactions: chemical production and consumption require reaction stoichiometry and extent or conversion.
No accumulation: tank filling, startup and shutdown require dynamic balances.
Consistent basis: mass fraction is not mole fraction. Mass and molar rates cannot be combined without molecular weights.
Same components: every component entering or leaving must be included, even trace components relevant to closure.
One complete unknown: multiple unknown stream flows or partially known stream compositions can be underdetermined; this version solves one complete missing stream.
Rounding: composition percentages within 0.05 percentage points of 100% are normalized before calculation.

Worked examples with complete calculations

Hand-check the built-in mixer, dilution of a caustic solution from 35 wt% to 15 wt%, and a two-outlet solids separation. Each example uses US customary units and shows the intermediate math. The examples explain each component balance and which cases require equations beyond the calculator's single-unknown-stream solver.

Read the material balance worked examples →

What the result means

A zero component residual confirms the entered streams satisfy the selected conservation equations. It does not establish whether the separator can reach the specified purity, whether the streams are physically feasible at the operating conditions, or whether the equipment is sized correctly.

For a nonreactive system, choosing an unknown outlet means its individual component rates are the known inlet rates minus the other known outlet rates. A negative calculated component means the known streams cannot be balanced by a physically valid outlet stream. The calculator rejects that case rather than reporting negative compositions.

Engineering aid for preliminary calculations and consistency checks. Verify units, process boundaries, and measurement uncertainty before design use.

Equation values and input guide

Choose mass or mole basis, define components, then enter every known stream’s rate and composition. Select one complete missing stream to calculate, or check all entered streams. A change of mass/mole basis requires consistent new data.

F: Total stream mass or molar rate in the selected unit, shared across all streams.
zi: Fraction of component i on the selected basis. Enter percentages in the form; 25% is 0.25 in the equations.
Fzi: Component rate: total stream rate multiplied by its component fraction, in the same rate units as F.
Σin, Σout: Sums over all inlet and outlet streams for the defined process boundary. Each component has its own balance.
Residual: Total inlet rate minus total outlet rate, evaluated overall and by component. Nonzero residual indicates unclosed entered data under the steady, nonreactive assumptions.

Use the unit selectors beside the inputs. Units shown in the equations must be consistent when checking the math by hand.

Material Balance Calculator