Two totals at your volume, the cheaper one, and the break-even volume where the cost lines cross. The delivery fee is the variable that pivots the decision — most "mulch calculators" omit it.

1 yd³ = 27 ft³

volume (Area + depth mode):
  volume_yd3 = area_ft² × (depth_in / 12) / 27

bagged:
  bags_needed  = ceil(volume_yd3 × 27 / bag_size_ft³)   ← rounded up to whole bags
  bagged_total = bags_needed × price_per_bag

bulk:
  bulk_total = volume_yd3 × price_per_yd3 + delivery_fee

break-even (continuous-bag approximation):
  effective_bag_$/yd³ = (27 / bag_size_ft³) × price_per_bag
  breakeven_yd3       = delivery_fee / (effective_bag_$/yd³ − price_per_yd3)

winner = lower of (bulk_total, bagged_total); savings = |difference|

Worked example: bag 2 ft³ @ $3.97, bulk $38/yd³, delivery $50 → effective bag rate $53.60/yd³, break-even ≈ 3.2 yd³. At 2 yd³ bagged wins ($107.19 vs $126.00); at 5 yd³ bulk wins ($240.00 vs $269.96).

The bagged total uses the real rounded-up bag count (a true purchase), while the break-even uses a smooth continuous-bag line so it lands on one clean rule-of-thumb figure. When the bulk per-yard rate never beats the per-bag rate, there is no positive crossover and bagged wins at every volume. Prices shown are illustrative placeholders, not sourced market rates.

The crossover tells you how to buy, not how much to buy or what to charge. Volume comes first, from the cubic-yard mulch takeoff or the same depth math applied to stone and soil, and once the yardage is settled what to charge to install and edge a mulch bed puts labor, delivery and margin around it. On a job with several materials moving at once, carry the bag and bulk lines into one takeoff sheet so the supplier order and the estimate cannot drift apart.

Formula: break-even yd³ = delivery_fee / ((27 / bag_ft³) × bag_price − bulk_$/yd³)

See Sources below