Margin and markup describe the same gross profit, but they answer different questions. Margin asks what share of selling price remains as profit. Markup asks how large that profit is compared with direct cost. Naming the denominator prevents a common pricing error.
Write profit once, then choose the base
Gross profit equals selling price minus direct cost. Margin is that profit divided by selling price; markup is the same profit divided by direct cost. With cost 60 and price 100, profit is 40, margin is 40/100 = 40%, and markup is 40/60 = 66.666667%.
Convert without inventing a price
A markup k converts to margin k/(1+k). A margin m converts to markup m/(1-m), with rates written as decimals. Thus 50% markup becomes 0.5/1.5 = 33.333333% margin, while 40% margin becomes 0.4/0.6 = 66.666667% markup.
Keep gross arithmetic separate from advice
The formulas prove a relationship between entered cost and price. They do not say whether the margin is good, whether every cost was included, or whether a price is competitive or compliant. Labor, overhead, taxes, fees, returns, and market conditions remain separate inputs and decisions.