Variance Analysis Formulas, With Worked Examples

Every variance analysis formula answers one question about the difference between plan and result. The total variance says how big the gap is; component formulas say which part came from volume, price, usage, rate or efficiency. This page collects the formulas used most often, with a single worked example that carries through so you can see how the pieces add to the total. It supports the method in budget variance analysis and is part of budgeting and forecasting.

The worked example setup

A hypothetical manufacturer has the following monthly standards and results.

Sign convention

Use the favorable positive convention: a variance is positive (F) when it improves profit, negative (U) when it reduces it. For revenue: Actual - Budget. For costs: Budget - Actual. State it on every report.

1. Total variance

Total variance = Actual - Budget
Percent variance = Total variance / Budget

Revenue: $188,100 - $200,000 = -$11,900, or -5.95 percent. The total shows size but not cause.

2. Flexible budget variance

A flexible budget restates the budget at the actual activity level.

Flexible budget = Budget cost per unit × Actual units
Flexible budget variance = Flexible budget - Actual cost
Volume variance (activity) = Original budget - Flexible budget

Materials: original budget for 4,000 units is 4,000 × 2 × $8 = $64,000. Flexible budget for 3,800 units is 3,800 × 2 × $8 = $60,800. Actual is 7,750 × $8.20 = $63,550.

• Activity variance (favorable): $64,000 - $60,800 = $3,200 (lower volume means lower cost).
• Flexible budget variance (unfavorable): $60,800 - $63,550 = -$2,750.
• Total: $64,000 - $63,550 = $450 favorable, which hides the real overrun of $2,750.

See flexible budgets.

3. Sales volume and price variances

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

Volume: (3,800 - 4,000) × $50 = -$10,000. Price: ($49.50 - $50.00) × 3,800 = -$1,900. Total: -$11,900. The two components add to the total, which is the check.

With multiple products, add a mix variance. See price-volume-mix analysis.

4. Sales margin variance

When cost matters, measure on contribution margin rather than revenue.

Sales volume margin variance = (Actual units - Budget units) × Budget margin per unit

If the budget margin per unit is $50 - $30 = $20, the volume margin variance is (3,800 - 4,000) × $20 = -$4,000. Revenue volume variance was -$10,000, but the profit effect of lost volume is only $4,000 because variable costs also fall. For profit analysis, use the margin version.

5. Direct materials variances

Material price variance = (Standard price - Actual price) × Actual quantity
Material usage variance = (Standard quantity allowed - Actual quantity) × Standard price

• Standard quantity allowed = 3,800 × 2 = 7,600 kg.
• Price: ($8.00 - $8.20) × 7,750 = -$1,550 (U).
• Usage: (7,600 - 7,750) × $8.00 = -$1,200 (U).
• Total: -$2,750 (U). Check: $60,800 - $63,550 = -$2,750.

6. Direct labor variances

Labor rate variance       = (Standard rate - Actual rate) × Actual hours
Labor efficiency variance = (Standard hours allowed - Actual hours) × Standard rate

• Standard hours allowed = 3,800 × 0.5 = 1,900 hours.
• Rate: ($24.00 - $25.00) × 1,960 = -$1,960 (U).
• Efficiency: (1,900 - 1,960) × $24.00 = -$1,440 (U).
• Total: -$3,400 (U). Check: standard cost of actual output is 1,900 × $24 = $45,600; actual cost is 1,960 × $25 = $49,000; difference is $3,400.

7. Overhead variances

Variable overhead

Variable overhead spending variance    = (Standard rate - Actual rate) × Actual hours
Variable overhead efficiency variance  = (Standard hours allowed - Actual hours) × Standard rate

Suppose the standard variable overhead rate is $5.00 per labor hour and the actual rate is $5.10 per hour.

• Spending: ($5.00 - $5.10) × 1,960 = -$196 (U).
• Efficiency: (1,900 - 1,960) × $5.00 = -$300 (U).

Fixed overhead

Fixed overhead spending variance = Budgeted fixed overhead - Actual fixed overhead

$10,000 - $10,500 = -$500 (U).

Summary of the example

The revenue variances total -$11,900 and the cost variances (materials -$2,750, labor -$3,400, variable overhead -$496, fixed overhead -$500) total -$7,146. The cost variances are measured against flexed standards, so the revenue volume effect must be handled on a margin basis when assessing profit impact. The arithmetic: -$2,750 + -$3,400 = -$6,150; adding -$496 gives -$6,646; adding -$500 gives -$7,146.

How to interpret pairs of variances

When two variances pull in opposite directions, look at the combined effect. The question is whether the trade-off was intended and worthwhile.

Mix variance: when several products are sold

With more than one product, the volume variance at the average price hides a mix effect. Take a separate example. Budget: Product A 2,000 units at $60 and Product B 2,000 units at $40, so 4,000 units and $200,000 of revenue, an average price of $50. Actual: Product A 1,500 units at $60 and Product B 2,300 units at $40, so 3,800 units and revenue of $90,000 + $92,000 = $182,000. Prices were as budgeted.

Volume variance = (Actual total units - Budget total units) × Budget average price
Mix variance    = Σ (Actual units of product - Actual total units × Budget mix %) × Budget price of product
Price variance  = Σ (Actual price - Budget price) × Actual units

• Volume: (3,800 - 4,000) × $50 = -$10,000
• Mix: budget mix is 50/50, so the expected units at the actual total are 1,900 each. Product A: (1,500 - 1,900) × $60 = -$24,000. Product B: (2,300 - 1,900) × $40 = +$16,000. Mix = -$8,000
• Price: $0
• Total: -$10,000 - $8,000 = -$18,000, which equals $182,000 - $200,000.

The business sold fewer units overall and shifted toward the lower-priced product, which hurt revenue by $8,000 more than the volume effect alone. When margins differ between products, the mix effect on profit can be larger still. See price-volume-mix analysis.

Setting up the calculation in a spreadsheet

A clean layout makes the formulas repeatable.

Include the check column in every variance workbook. A non-zero check shows an error in a base or a sign before the report reaches a manager.

Percentage and ratio measures

Variance % = Variance / Budget
Margin variance % = (Actual margin % - Budget margin %)
Cost per unit variance = Actual cost per unit - Standard cost per unit

In the example, actual labor cost per unit is $49,000 / 3,800 = $12.89 against a standard of $12.00, a difference of $0.89 or 7.4 percent.

Common errors

• Using the original budget to compare costs at a different volume.
• Mixing signs between revenue and cost variances.
• Applying the wrong base (actual vs standard price or quantity).
• Treating components as independent when they interact.
• Ignoring mix when there are multiple products.
• Not checking that components add to the total.

For the link between these formulas and the unit-level margins of what you sell, see unit economics.

Related guides

To go deeper on revenue effects across several products, read price-volume-mix analysis, and to understand sign conventions, see favorable vs. unfavorable variances.

FAQs

What is the formula for variance analysis?

Variance equals actual minus budget for revenue, and budget minus actual for costs when using favorable positive. Component formulas break it into volume, price, usage, rate and efficiency effects.

What is the sales price variance formula?

(Actual price - Budget price) × Actual units.

What is the material usage variance formula?

(Standard quantity allowed for actual output - Actual quantity used) × Standard price.

Why compare against a flexible budget?

Because the original budget was set for a different volume. A flexible budget shows whether costs were controlled for the activity that actually happened.

How do I check my variance calculations?

The components should add to the total variance. If they do not, there is an error in the base or the sign.