formulas for variance analysis

variance formulas/equations which can help you calculate variances for direct materials, direct labor, and factory overhead.

1. Direct materials variances formulas
2. Direct labor variances formulas
3. Factory overhead variances formulas

Direct Materials Variances:

Materials purchase price variance Formula:
Materials purchase price variance = (Actual quantity purchased × Actual price) – (Actual quantity purchased × Standard price)

Materials price usage variance formula:
Materials price usage variance = (Actual quantity used × Actual price) – (Actual quantity used × Standard price)

materials quantity/usage variance formula:Materials price usage variance = (Actual quantity used × Standard price) – (Standard quantity allowed × Standard price)

Materials mix variance formula:(Actual quantities at individual standard materials costs) –  (Actual quantities at weighted average of standard materials costs)

Materials yield variance formula:(Actual quantities at weighted average of standard materials costs) –  (Actual output quantity at standard materials cost)

Direct Labor Variances:

Direct labor rate/price variance formula:
(Actual hours worked × Actual rate) – (Actual hours worked × Standard rate)

Direct labor efficiency/usage/quantity formula:(Actual hours worked × Standard rate) – (Standard hours allowed × Standard rate)

Direct labor yield variance formula:(Standard hours allowed for expected output × Standard labor rate) – (Standard hours allowed for actual output × Standard labor rate)

Factory Overhead Variances:

Factory overhead controllable variance formula:
(Actual factory overhead) – (Budgeted allowance based on standard hours allowed*)

Factory overhead volume variance:(Budgeted allowance based on standard hours allowed*) – (Factory overhead applied or charged to production**)

Factory overhead spending variance:(Actual factory overhead) – (Budgeted allowance based on actual hours worked***)

Factory overhead idle capacity variance formula:(Budgeted allowance based on actual hours worked***) – (Actual hours worked × Standard overhead rate)

Factory overhead efficiency variance formula:
(Actual hours worked × Standard overhead rate) – (Standard hours allowed for expected output × Standard overhead rate)

Variable overhead efficiency variance formula:(Actual hours worked × Standard variable overhead rate) – (Standard hours allowed × Standard variable overhead rate)

Variable overhead efficiency variance formula:(Actual hours worked × Fixed overhead rate) – (Standard hours allowed × Fixed overhead rate)

Factory overhead yield variance formula:
(Standard hours allowed for expected output × Standard overhead rate) – (Standard hours allowed for actual output × Standard overhead rate)

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*Fixed overhead budgeted + Standard hours allowed × Standard variable overhead rate

**Standard hours allowed for actual production × Standard overhead rate

***Fixed overhead budgeted + Actual hours worked × Standard variable overhead rate

Sales value variance	(budgeted quantity x standard selling price) less (actual quantity x actual selling price)
Sales price variance	(standard selling price-actual selling price) x actual quantity sold
Sales volume variance	(budgeted quantity-actual quantity) x standard selling price or standard profit or standard contribution
Sales margin variance	(budgeted quantity x standard profit)- (actual quantity x actual profit)
Sales contribution variance	(budgeted quantity x standard contribution)-(actual quantity x actual contribution)
Sales allowance variance	(budgeted allowance-actual allowance) x actual quantity sold
Sales mix variance	(standard mix-actual mix) x standard selling price or standard profit or standard contribution
Sales quantity variance	(budgeted quantity-actual quantity in standard mix) x standard price or standard profit or standard contribution