Sword value

What a blade is worth to the dragon, and why two swords at the same grade can be worth very different amounts.

A fresh sword is worth 320 G and every level multiplies that by 1.5, so a plain blade is worth 2,430 G at +5, 18,453 G at +10 and 1,064,082 G at +20. That's the floor. Greats, relics and merchant lines all push a blade above it, and the formula the game uses tells you which bonuses grow with the sword and which don't.

The formula

(base × 1.5grade + flat) × multipliers
rounded to the nearest gold
Base
320 G, or 640 G for the merchant's World Tree, Fishblade and Funerary blades. Charcoal Pouch (+80), Pocket Hearth (+20 per tribute paid), Golden Cog (+30 per Success), Soot Censer (+20 per change of result) and Eternal Seed (+40 per Hold) add to it.
Multipliers
Permanent on the sword (Cracked Bell, Double Knot, Cold Teacup, Bound Idol, Dragon Heart, Bell Collar, and the 0.6 from Phoenix Ash) or tied to the shelf (Iron Signet x1.15, Thorn Weight x1.1, Black Iron Stone x1.3 from +8, Dragon Signet x1.5 from +12).

The order matters. Anything added to base is multiplied by 1.5 for every level the sword gains afterwards, so Charcoal Pouch's 80 G is worth 4,613 G on a +10 blade. A flat bonus stays exactly what it says. That's why the base relics climb so well on a sword you plan to push high.

Why a Great is worth more than two levels

Two levels multiply the base by 1.5 twice, which is 2.25. A Great instead sets the value to 2.5 times what it was and stores the difference on the sword for good, so the bonus is still there after a later Damage. With no relics:

+8 on Successes, then a Great to +10
20,503 G
+10 on Successes alone
18,453 G
The Great blade knocked back to +9 by a Damage
13,669 G
A plain +9
12,302 G

Damage and Break

Damage takes a level, which divides the base part by 1.5 again. Flat bonuses and the multipliers are untouched, and Cracked Crown and Iron Comb even turn the lost level into a flat bonus. A Break leaves nothing unless Undertaker's Chalice is on the shelf, which keeps 30% of the highest value the sword ever had as scrap and puts it in the tribute window for you.

Base value by grade

A merchant line is the World Tree, Fishblade or Funerary blade, which starts from double the base.

GradeDelivered swordMerchant lineGradeDelivered swordMerchant line
+0320640+16210,189420,378
+1480960+17315,284630,567
+27201,440+18472,925945,851
+31,0802,160+19709,3881,418,776
+41,6203,240+201,064,0822,128,164
+52,4304,860+211,596,1233,192,246
+63,6457,290+222,394,1854,788,370
+75,46810,935+233,591,2777,182,555
+88,20116,403+245,386,91610,773,832
+912,30224,604+258,080,37416,160,748
+1018,45336,906+2612,120,56124,241,122
+1127,67955,358+2718,180,84136,361,682
+1241,51983,038+2827,271,26254,542,524
+1362,278124,556+2940,906,89381,813,785
+1493,417186,835+3061,360,339122,720,678
+15140,126280,252+3192,040,508184,081,017

The odds calculator shows the value of any grade with your value relics on the shelf, and the forge simulator tracks it strike by strike, Greats and procs included.