The midpoint (arc) elasticity formula

There are two common ways to calculate elasticity: point (tiny changes around a single price) and arc (a change from one price to another). In real life, pricing experiments aren’t “infinitesimal” — they’re a step from (P₁, Q₁) to (P₂, Q₂). That’s why this calculator uses the midpoint method, which is more stable and symmetric.

• %ΔQ = (Q₂ − Q₁) ÷ ((Q₁ + Q₂) / 2)
• %ΔP = (P₂ − P₁) ÷ ((P₁ + P₂) / 2)

• E = (%ΔQ) ÷ (%ΔP)

Elasticity is usually negative (because price goes up while quantity goes down). In business conversations, people often discuss the magnitude (|E|). This calculator shows both: the signed value (direction) and |E| (strength).

• Revenue before = P₁ × Q₁
• Revenue after = P₂ × Q₂
• ΔRevenue = Revenue after − Revenue before

Revenue impact is not profit. If you want profit impact, you’ll also need unit costs, variable fulfillment costs, and (often) changes in support burden and churn. Use this tool first to understand demand sensitivity, then layer in unit economics.

Three quick scenarios you can copy

These examples show the intuition behind elasticity. You can plug them into the calculator by typing values or by using the sliders.

• P₁ = $50, Q₁ = 1,000
• P₂ = $55 (+10%), Q₂ = 850 (−15%)
• Result: |E| is typically > 1 → demand is relatively elastic → revenue may fall unless value/packaging improves.

• P₁ = $10, Q₁ = 10,000
• P₂ = $11 (+10%), Q₂ = 9,600 (−4%)
• Result: |E| < 1 → inelastic → a modest price increase can raise revenue.

• P₁ = $100, Q₁ = 500
• P₂ = $70 (−30%), Q₂ = 900 (+80%)
• Result: |E| can be very high → promo is demand-creating (but verify margin + fulfillment capacity).

A practical way to use elasticity: run a few small tests (e.g., +5%, +10%, −10%) and compare estimates by segment. If results swing wildly, it’s a signal your market has multiple customer types or your messaging/offer changed with price.

Turn a number into a decision

Elasticity is a sensitivity score, not a moral judgment. An “elastic” product isn’t bad — it just means customers have more alternatives or the value isn’t clearly differentiated at that price.

• |E| < 0.3: Very inelastic (rare; usually essentials or locked-in contracts)
• 0.3 ≤ |E| < 1.0: Inelastic (raising price tends to increase revenue)
• |E| ≈ 1.0: Unit elastic (revenue stays roughly similar for small moves)
• 1.0 < |E| ≤ 2.0: Elastic (lowering price tends to increase revenue)
• |E| > 2.0: Very elastic (pricing is a major driver; consider differentiation, bundles, or segmentation)

• If |E| < 1: You have pricing power. Test a small increase, but watch churn and support tickets.
• If |E| ≈ 1: Focus on packaging, positioning, or upsells — revenue gains may be limited by price alone.
• If |E| > 1: Price is sensitive. Consider segmentation (student plan, annual discounts), bundles, or improving perceived value.

For viral sharing: screenshot your result and ask, “Is my market elastic?” — then compare by channel (organic vs paid), customer type (new vs existing), or geography. The most valuable insight is often that elasticity is not one number.

Frequently Asked Questions

• Which elasticity formula is this?

  The midpoint (arc) method. It compares percent changes using the average of the two points, which makes the result more stable and less sensitive to whether you treat the baseline as P₁ or P₂.

• Why is my elasticity negative?

  For most products, price and quantity move in opposite directions. A negative E is normal. Many dashboards discuss |E| (the magnitude) because it’s easier to reason about “how sensitive” demand is.

• What if quantity increases when price increases?

  That can happen (Veblen goods, prestige effects, or when a price increase signals quality). In that case E can be positive — interpret it carefully and validate with more data.

• How big should my price test be?

  Small tests (±5% to ±15%) usually produce cleaner signals. Huge changes can alter positioning, attract deal‑seekers, or trigger competitor responses — which changes elasticity itself.

• Does elasticity equal profit impact?

  No. Elasticity helps you estimate demand response. Profit depends on unit costs, variable expenses, conversion rates, support load, churn, and capacity constraints.

• Should I use units sold, signups, or conversions for Q?

  Use the metric that directly responds to price for the decision you’re making. For SaaS, Q could be new subscriptions, paid conversions, or retained customers after a renewal price change.

• My result is extreme (like |E| > 10). Is that possible?

  It can happen when the denominator (%ΔP) is very small or when demand changed for reasons other than price (seasonality, marketing, stockouts). Try larger test sizes or isolate price effects better.

• How do I estimate elasticity from historical data?

  Identify periods where price changed while other factors stayed relatively stable. Then compare (P₁, Q₁) to (P₂, Q₂). For higher accuracy, use regression with controls (seasonality, spend, channel mix).

• What’s a “good” elasticity?

  There isn’t one. Inelastic demand means pricing power; elastic demand means customers are price-sensitive. “Good” depends on your strategy: premium differentiation vs volume growth.

• Can I share results with my team?

  Yes — use the share buttons or copy your result text. Saved snapshots stay on this device only.

Make this calculator spread

If you want this page to perform well socially, use it like a mini “pricing experiment story”:

• Hook: “We raised prices by X%. Want to guess what happened to demand?”
• Reveal: Share the elasticity magnitude (|E|) and revenue delta.
• Debate prompt: “Is my market inelastic or do I need better differentiation?”
• Segment challenge: “Run this separately for organic vs paid and compare.”

Tip: A screenshot of the result box plus a one-sentence context (industry + offer) gets more replies than a raw link.