Learn · Incremental games

Cost curves in incremental games

In an incremental game nearly everything can be bought again, and each one costs more than the last. How fast that price climbs, the cost curve, sets the pace of the whole game: when it flies, and when it stalls. Here are the first 100 purchases of the same thing, priced six ways.

Prices that add Linear Each one costs 5 more than the last: the 100th costs 505. Details
Prices that add Polynomial The price follows the square of the count: the 100th costs 100K. Details
Prices that multiply Exponential, ×1.07 Each one costs 7% more than the last: the 100th costs 8.11K. Details
Prices that multiply Exponential, ×1.15 Each one costs 15% more than the last: the 100th costs 10.2M. Details
Prices that multiply Stepped Ten at one price, then ten times more: the 100th costs 10B. Details
Faster than multiplying Super-exponential The multiplier itself keeps growing: the 100th costs 40.3T. Details
Pick a curve

Each picture shows the price of purchases 1 to 100. Every faint line is ten times the one below, so a price that keeps multiplying by the same amount climbs in a straight line.

Prices that add

Each price is the last one plus some amount. In proportion, the rises shrink as the price grows: 10 to 15 is half again, but 500 to 505 is just 1%.

150100101K100K10M1B100B

Linear

Also called arithmetic, flat step

Every purchase costs the same amount more than the last. The income from what you've bought grows just as fast, so a game priced this way keeps a steady pace and never slows down.

Price
10 + 5 × owned
100th costs
505
×1,000 by
The 1,999th purchase
Good for
Things bought a handful of times, and levels that should never stall
150100101K100K10M1B100B

Polynomial

Also called power curve, quadratic, cubic

The price follows a power of the count, here its square. It climbs much faster than linear early on, but its steps shrink in proportion, so in the long run any multiplying price overtakes it.

Price
10 × (owned + 1)²
100th costs
100K
×1,000 by
The 32nd purchase
Good for
RPG levels and stat upgrades bought a few dozen times

Prices that multiply

Prices multiply: by a little each purchase, or by a lot every ten. Gentle at first, they eventually outrun any price that adds, and most idle games price their generators this way.

150100101K100K10M1B100B

Exponential, ×1.07

Also called geometric, compound

Each purchase costs 7% more than the last, so the price doubles about every ten. Here it starts out cheaper than the linear curve, passes it around the 50th purchase, and then pulls away for good.

Price
10 × 1.07^owned
100th costs
8.11K
×1,000 by
The 104th purchase
Good for
Generators bought hundreds of times, in a game with a long first run
150100101K100K10M1B100B

Exponential, ×1.15

Also called geometric, compound

Each purchase costs 15% more, doubling the price about every five. Each new generator matters for a while and then gives way to the next tier, which is why the shop keeps growing.

Price
10 × 1.15^owned
100th costs
10.2M
×1,000 by
The 51st purchase
Good for
A shop with many tiers, where the newest one should take over
150100101K100K10M1B100B

Stepped

Also called bought in tens, tiered price

The price holds for ten purchases, then jumps ten times higher. On average it multiplies like an exponential, but players buy in sets and aim for the next step.

Price
10 × 10^⌊owned ÷ 10⌋
100th costs
10B
×1,000 by
The 31st purchase
Good for
Pairing with a reward for each full set, like a ×2 per ten

Faster than multiplying

The multiplier itself grows, so the climb gets steeper with every purchase.

150100101K100K10M1B100B

Super-exponential

Also called cost scaling, accelerating price

Each price is ×1.05 the last, and that multiplier grows 0.5% with every purchase. It works as a ceiling without a hard limit: past a point no realistic income keeps up, so the player turns to something else.

Price
10 × 1.05^owned × 1.005^(owned × (owned − 1) ÷ 2)
100th costs
40.3T
×1,000 by
The 46th purchase
Good for
Capping an upgrade softly instead of with a hard limit

Side by side

The same purchases on each curve, all starting at 10 coins.

Curve 10th25th50th100th First 100 together
Linear 55130255505 25.8K
Polynomial 1K6.25K25K100K 3.38M
Exponential, ×1.07 18512758.11K 124K
Exponential, ×1.15 352869.42K10.2M 78.3M
Stepped 101K100K10B 111B
Super-exponential 1912838.5K40.3T 97.9T