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Cost and Management Accounting · Standard Costing

Overhead Variances (Variable and Fixed): Formulas and Solved Problems

Updated 4 October 2026 · Fact-checked

Overhead variances compare standard overhead absorbed for actual output with actual overhead. Variable overhead splits into expenditure and efficiency variances. Fixed overhead splits into expenditure and volume, and volume splits into efficiency, capacity and calendar. Find the standard rate, standard hours for actual output, actual hours and budget, then apply each formula and mark F or A.

Understand Overhead Variances (Variable and Fixed)

An overhead variance is the difference between the overhead that should have been charged to actual output at standard and the overhead actually incurred. If standard overhead absorbed is higher than actual, the variance is Favourable (F). If it is lower, the variance is Adverse (A).

Start with variable overheads. They change with activity, so the standard rate per hour (or per unit) is simple. Two things can go wrong. You may spend more per hour than planned (expenditure variance). Or you may use more hours than the standard for the actual output (efficiency variance). Together they make the variable overhead cost variance.

Fixed overheads do not change with output within the relevant range. So the budget is a fixed amount, and the standard rate is Budgeted fixed overhead ÷ Budgeted output (or budgeted hours). Fixed overhead is absorbed at this rate on the output you actually make. Two things can go wrong. You may spend more than the budget (expenditure variance). Or you may produce less than budgeted, so less overhead is absorbed (volume variance).

The volume variance has causes behind it. Workers may be slower or faster than standard (efficiency). The plant may run fewer or more hours than planned (capacity). The month may have fewer or more working days than budgeted (calendar). That is why volume = efficiency + capacity + calendar. If the question gives no day data, ignore calendar and use volume = efficiency + capacity.

In all cases, the logic is the same: standard on one side, actual or budget on the other, and the sign tells you F or A.

Key rules to remember

Standard rate (fixed overhead)
Standard rate per hour = Budgeted fixed overhead ÷ Budgeted hours; Standard rate per unit = Budgeted fixed overhead ÷ Budgeted output
Use the rate that matches the base given in the question (hours or units).
Standard hours for actual output
SH = Actual output × Standard hours per unit
Needed for every efficiency variance and to find absorbed overhead.
Variable overhead cost variance
Standard VOH for actual output − Actual VOH, where Standard VOH = SH × Standard rate per hour
Equals expenditure variance + efficiency variance.
Variable overhead expenditure variance
(Actual hours × Standard rate per hour) − Actual VOH
Also called budget variance. Positive means F.
Variable overhead efficiency variance
Standard rate per hour × (Standard hours for actual output − Actual hours)
Fewer actual hours than standard means F.
Fixed overhead cost variance
Absorbed FOH − Actual FOH, where Absorbed FOH = Actual output × Standard rate per unit (or SH × rate per hour)
Equals expenditure variance + volume variance.
Fixed overhead expenditure variance
Budgeted FOH − Actual FOH
Uses the budget, not the absorbed amount.
Fixed overhead volume variance
Absorbed FOH − Budgeted FOH = Standard rate per unit × (Actual output − Budgeted output)
Equals efficiency + capacity + calendar variances.
Fixed overhead efficiency variance
Standard rate per hour × (Standard hours for actual output − Actual hours)
Same form as the variable overhead efficiency variance.
Fixed overhead capacity variance
Standard rate per hour × (Actual hours − Revised budgeted hours)
Without calendar data, use budgeted hours instead of revised budgeted hours.
Fixed overhead calendar variance
Standard rate per hour × (Revised budgeted hours − Budgeted hours), where Revised budgeted hours = Budgeted hours × Actual days ÷ Budgeted days
More actual days than budgeted gives F; fewer gives A.

How to solve Overhead Variances (Variable and Fixed) questions

Use the same routine for every overhead question. Do the base data first, then the variances, then check the totals.

  1. 1Separate the data into budget (budgeted output, hours, days, overhead), standard (hours per unit, rate) and actual (output, hours, days, overhead).
  2. 2Compute the standard rate: budgeted fixed overhead ÷ budgeted hours or units. For variable overhead, the rate is usually given.
  3. 3Compute standard hours for actual output (actual output × standard hours per unit). Compute revised budgeted hours if actual and budgeted days differ.
  4. 4Compute the amounts you will reuse: absorbed overhead (standard hours × rate) and, for fixed overhead, the budgeted overhead.
  5. 5Apply each formula in the same direction (standard or budget minus actual, or standard hours minus actual hours) so the sign gives F or A directly.
  6. 6Label every answer F or A.
  7. 7Check: expenditure + efficiency = variable cost variance; expenditure + volume = fixed cost variance; efficiency + capacity + calendar = volume variance. Fix any mismatch before moving on.

Quickest way: Rate-and-hours table with a three-line check

When to use it: Use it for any numerical with several variances, especially when the MCQ or written part asks for only one or two of them.

  1. Write four lines at the top: standard rate, standard hours (SH), actual hours (AH), revised budgeted hours (RBH) if days are given.
  2. Write the variances as rate × hour differences. Efficiency = rate × (SH − AH). Capacity = rate × (AH − RBH). Calendar = rate × (RBH − Budgeted hours). Add them to get volume.
  3. Get expenditure straight from the money figures: budget (or AH × rate for variable) minus actual.
  4. Add expenditure and volume to get the cost variance. If it matches absorbed minus actual, you are done.
  5. For MCQs, find only the variance asked. Fixed overhead volume needs only absorbed overhead and budget. Variable expenditure needs only AH, the rate and actual overhead.
  6. In written answers, show the rate calculation and each formula line separately and end with a small summary of all variances with F or A. This earns step marks even if one figure is wrong.

Common mistakes in Overhead Variances (Variable and Fixed)

  • Using absorbed overhead instead of budgeted overhead in the fixed overhead expenditure variance.

    Students copy the pattern from the cost variance, where absorbed overhead is used.

    Fix: Fixed expenditure variance = Budgeted FOH − Actual FOH. Absorbed overhead appears only in cost and volume variances.

  • Using actual hours at the standard rate as the base for the variable expenditure variance but forgetting it in the efficiency variance, or mixing the two.

    Both use the rate per hour, so the hour bases get confused.

    Fix: Expenditure uses actual hours (AH × rate − actual VOH). Efficiency uses the difference between standard hours for actual output and actual hours.

  • Calculating standard hours from budgeted output, not actual output.

    Budgeted figures sit at the top of the question and look like the standard.

    Fix: Standard hours for actual output = actual output × standard hours per unit. Budgeted hours are used only for the rate and the budget.

  • Ignoring the calendar variance, or computing capacity against budgeted hours when days differ.

    Students skip the days data, or do not know revised budgeted hours.

    Fix: If actual and budgeted days differ, calculate revised budgeted hours = budgeted hours × actual days ÷ budgeted days. Capacity uses it, and calendar is the gap between it and budgeted hours.

  • Wrong sign: labelling a variance F when it is A.

    Formulas are written in different directions for different variances.

    Fix: Always write the formula as favourable-if-positive (standard or budget minus actual; SH minus AH; AH minus RBH). Then the sign decides F or A.

  • Treating fixed overhead as varying with output when computing the budget.

    Students apply a variable overhead mindset to the flexed budget.

    Fix: Budgeted fixed overhead stays at the budget amount (for the period) regardless of actual output. Only absorbed overhead moves with output.

Worked examples

Example 1

Budgeted output is 1,000 units and each unit has a standard of 4 hours. The standard variable overhead rate is ₹5 per hour. Actual output is 900 units, actual hours worked are 3,750 and actual variable overhead is ₹20,000. Calculate the variable overhead cost, expenditure and efficiency variances.

Show the solution
  1. Standard hours for actual output = 900 × 4 = 3,600 hours.
  2. Standard variable overhead for actual output = 3,600 × ₹5 = ₹18,000.
  3. Cost variance = ₹18,000 − ₹20,000 = ₹2,000 (A).
  4. Expenditure variance = (3,750 × ₹5) − ₹20,000 = ₹18,750 − ₹20,000 = ₹1,250 (A).
  5. Efficiency variance = ₹5 × (3,600 − 3,750) = ₹5 × (−150) = ₹750 (A).
  6. Check: ₹1,250 (A) + ₹750 (A) = ₹2,000 (A), which equals the cost variance.

Answer: Variable overhead cost variance ₹2,000 (A); expenditure variance ₹1,250 (A); efficiency variance ₹750 (A).

Example 2

Budget for a month: fixed overhead ₹2,40,000; output 10,000 units at 2 hours per unit (20,000 hours); 25 working days. Actual: fixed overhead ₹2,45,000; output 9,700 units; hours worked 19,000; 24 working days. Calculate the fixed overhead cost, expenditure, volume, efficiency, capacity and calendar variances.

Show the solution
  1. Standard rate per hour = ₹2,40,000 ÷ 20,000 = ₹12. Standard rate per unit = ₹24.
  2. Standard hours for actual output = 9,700 × 2 = 19,400 hours.
  3. Absorbed overhead = 19,400 × ₹12 = ₹2,32,800.
  4. Revised budgeted hours = 20,000 × 24 ÷ 25 = 19,200 hours.
  5. Cost variance = ₹2,32,800 − ₹2,45,000 = ₹12,200 (A).
  6. Expenditure variance = ₹2,40,000 − ₹2,45,000 = ₹5,000 (A).
  7. Volume variance = ₹2,32,800 − ₹2,40,000 = ₹7,200 (A).
  8. Efficiency variance = ₹12 × (19,400 − 19,000) = ₹4,800 (F).
  9. Capacity variance = ₹12 × (19,000 − 19,200) = ₹2,400 (A).
  10. Calendar variance = ₹12 × (19,200 − 20,000) = ₹9,600 (A).
  11. Check: ₹4,800 (F) − ₹2,400 − ₹9,600 = ₹7,200 (A), which equals the volume variance. Also ₹5,000 (A) + ₹7,200 (A) = ₹12,200 (A).

Answer: Cost ₹12,200 (A); expenditure ₹5,000 (A); volume ₹7,200 (A); efficiency ₹4,800 (F); capacity ₹2,400 (A); calendar ₹9,600 (A).

Exam tips

  • In written answers, show the standard rate and standard hours before the variances. Examiners give marks for these workings even if a later figure is wrong.
  • Always end with a summary and the reconciliation check: efficiency + capacity + calendar = volume, and expenditure + volume = cost variance.
  • If the question gives no working days, leave out calendar and use volume = efficiency + capacity. Do not invent days.
  • Read the base carefully. Some questions give the overhead rate per unit, others per hour. Use the one given and convert only when you need hours.
  • Overhead variances are often asked inside a larger standard costing question with material, labour and sales. Do the overhead part last, since it reuses hours from the labour part.

Practice questions from Standard Costing

Overhead Variances (Variable and Fixed) in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Overhead Variances (Variable and Fixed): frequently asked questions

What is the difference between fixed overhead expenditure and volume variance?

Expenditure variance compares the budgeted fixed overhead with the actual amount spent. Volume variance compares the overhead absorbed on actual output with the budget. One is about spending, the other is about how much was produced.

How do I calculate the fixed overhead capacity variance?

Capacity variance = standard rate per hour × (actual hours − revised budgeted hours). If the question has no calendar data, use budgeted hours in place of revised budgeted hours. A positive result is favourable.

When do I calculate the calendar variance?

Calculate it when actual working days differ from budgeted days. Revised budgeted hours = budgeted hours × actual days ÷ budgeted days. Calendar variance = standard rate per hour × (revised budgeted hours − budgeted hours).

Is variable overhead efficiency variance the same as fixed overhead efficiency variance?

The formula has the same form: rate per hour × (standard hours for actual output − actual hours). The rate differs, since one uses the variable overhead rate and the other the fixed overhead rate.

Does the variable overhead have a volume variance?

No. Variable overhead moves with activity, so the standard overhead for actual output already reflects the level of output. Only fixed overhead has volume, capacity and calendar variances.