Variance analysis: types, formulas and one worked example

Variance analysis compares actual results with the budget or standard and splits the difference into the causes behind it. A sales shortfall of $2,320 is not one fact but two: $10,000 lost on 400 fewer units, and $7,680 gained on a higher price. The method is the same on every line, and the test is always that the parts add back to the total.

What variance analysis means

A variance is actual minus budget, or actual minus standard. On its own it says only that something changed. Variance analysis asks why, by splitting it into a quantity effect and a price effect, each computed while holding the other one fixed.

Every variance gets a direction. Favorable means it increases profit compared with budget: more revenue, or less cost. Unfavorable means it reduces profit. UK texts call an unfavorable variance adverse, so a UK report reads "favorable and adverse" in British spelling where a US one reads favorable and unfavorable.

Two baselines are common. A budget is the plan for the period: revenue and cost by line. A standard is the expected cost of one unit: so many pounds of material at so much per pound. Standard costing sets the standards; variance analysis compares actual costs with them, as the OpenStax managerial accounting text (Rice University) sets out.

The main types

Sales mix belongs with volume: when products with different margins sell in different proportions from budget, profit moves even if total units are on plan. Mix needs its own split, which a price-volume-mix analysis covers; this page keeps to price and volume.

The formulas

Variance = Actual − Budget (favorable when it increases profit)

Sales volume variance = (Actual units − Budget units) × Budget price

Sales price variance = (Actual price − Budget price) × Actual units

Material price variance = (Actual price − Standard price) × Actual quantity

Material usage variance = (Actual quantity − Standard quantity for actual output) × Standard price

The pattern is fixed: the quantity variance is valued at the budget or standard price, and the price variance is measured on the actual quantity. Change that order and the parts stop adding up.

On a cost line, a positive result is unfavorable; on a revenue line, a positive result is favorable. Label every figure F or U rather than relying on the sign.

Worked example: sales variance

One product, one month, in USD:

Revenue is $2,320 below budget. Split it:

• Volume variance: (9,600 − 10,000) × 25.00 = −$10,000, unfavorable. Selling 400 fewer units at the budget price would have cost $10,000.
• Price variance: (25.80 − 25.00) × 9,600 = +$7,680, favorable. Each unit sold for 80 cents more.

In Excel, with budget units and price in B2 and C2 and actual units and price in B3 and C3:

Volume variance:  =(B3-B2)*C2
Price variance:   =(C3-C2)*B3
Total variance:   =B3*C3-B2*C2

The story is not "sales were slightly down". It is that a price increase held but cost 4% of volume. Which customers paid the higher price and which walked is the next question; price realization by customer answers it line by line, and the price variance entry gives the short definition.

Worked example: material cost variance

The standard is 2.0 lb of material per unit at $4.50 per lb, a standard cost of $9.00 per unit. Actual output was 9,600 units.

The standard quantity is 9,600 × 2.0 = 19,200 lb. Actual usage was 20,160 lb, or 2.1 lb per unit.

• Price variance: (4.70 − 4.50) × 20,160 = $4,032, unfavorable. Material cost 20 cents a pound more than standard.
• Usage variance: (20,160 − 19,200) × 4.50 = $4,320, unfavorable. The plant used 960 lb more than 9,600 units should take.

Price variance:  =(Actual_price-Std_price)*Actual_qty
Usage variance:  =(Actual_qty-Std_qty_per_unit*Units_made)*Std_price

Two different owners: purchasing answers for the price, production for the usage. A single "materials over by $8,352" line would have given neither of them anything to act on.

The check: the parts sum to the total

Every split has to add back to the variance it explains:

If the parts do not sum, the order is wrong somewhere: usually the price variance measured on budget quantity while volume is measured on actual, which counts the 400 units × $0.80 interaction twice or not at all. Build the check into the workbook as one cell that must be zero:

=(Volume_var+Price_var)-(Actual_revenue-Budget_revenue)

Budget variance analysis in a monthly reporting package

In a monthly package, budget variance analysis runs line by line down the P&L: budget, actual, variance in dollars, variance in percent, F or U. Three rules keep it useful.

Flex the budget for cost lines that move with volume. The original budget for materials was 10,000 × $9.00 = $90,000, so against it the overspend looks like $4,752. Against the budget flexed to 9,600 units it is $8,352. The $3,600 difference, 400 units × $9.00, is volume, not cost control.

Set a materiality threshold and write it down. Many finance teams only explain variances above both a percentage and a dollar amount, such as 5% and $25,000. The OpenStax chapter on how companies use variance analysis notes that managers are typically asked to explain any variance outside a set range, and that many companies require explanations for favorable variances as well as unfavorable ones.

Explain the cause, not the number. "Materials were $8,352 over budget" restates the table. "Steel cost 20 cents a pound more after the March contract, and scrap on line 2 added 960 lb" explains it. The SEC asks the same of public companies' MD&A, which "should not be merely a restatement of financial statement information in a narrative form", per its 2003 interpretive guidance. What makes a change an insight covers which variances earn a sentence, and how to read a forecast bridge shows the same split laid out as a chart.

Where it goes wrong

• The original budget instead of a flexed one. Comparing actual costs with a budget set for 10,000 units when 9,600 were made hides $3,600 of the overrun inside volume.
• Sign conventions that flip. Positive is favorable on revenue and unfavorable on cost; a report that colors by sign alone gets half its lines wrong.
• Commentary that restates. "Costs were $8,352 over" is the number again. The cause is price and usage, and who owns each.
• Parts that do not sum. Price measured on budget quantity and volume on actual quantity leave an unexplained interaction term.
• Ignoring mix. Two products at different margins can produce a profit variance even when total units are exactly on budget.

From variance to explanation

A variance explanation is the output Covirage is built to produce. Its tools split each variance into its causes from your uploaded ledger and budget and check that the parts sum to the total; the external AI model writes the commentary from those figures and never does the arithmetic. See cost variance analysis, and FP&A software alternatives for variance analysis if you are comparing tools. To set the comparison up, use the budget vs actual template, and for where variance work sits in finance, see what FP&A is.