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Nov 01, 2015 I've been using DMG pages 278 (Overall Damage Output) and 249 (Adjudicating Areas of Effect), which I've attached as images for clarity, along with my example spell - Vitriolic Sphere - from the Elemental Evil Player's Companion page 23. Vitriolic Sphere deals a total of 15d4 damage per target on a failed save. It explodes in a 20-foot radius.

• You can now switch between an expected success rate ─i.e: the chance of an attack to hit or a save to be failed─ of one half (what I originally used) or two thirds (based on the recommended values of the DMG, pages 283-284). The table now includes the base average result of the spell's damage roll.
• Jan 23, 2016  D&D 5E: Area of Effect On page 249 of the DMG, under Adjudicating Areas of Effect, it has this table with conversions for estimating how many targets are hit with an area of effect spell when using a battle grid.

Damage Rolls

Each weapon, spell, and harmful monster ability specifies the damage it deals. You roll the damage die or dice, add any modifiers, and apply the damage to your target. Magic weapons, special abilities, and other factors can grant a bonus to damage. With a penalty, it is possible to deal 0 damage, but never negative damage.

When attacking with a weapon, you add your ability modifier–the same modifier used for the attack roll–to the damage. A spell tells you which dice to roll for damage and whether to add any modifiers.

If a spell or other effect deals damage to more than one target at the same time, roll the damage once for all of them. For example, when a wizard casts fireball or a cleric casts flame strike, the spell's damage is rolled once for all creatures caught in the blast.

Critical Hits

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When you score a critical hit, you get to roll extra dice for the attack's damage against the target. Roll all of the attack's damage dice twice and add them together. Then add any relevant modifiers as normal. To speed up play, you can roll all the damage dice at once.

For example, if you score a critical hit with a dagger, roll 2d4 for the damage, rather than 1d4, and then add your relevant ability modifier. If the attack involves other damage dice, such as from the rogue'sSneak Attack feature, you roll those dice twice as well.

Damage Types

Different attacks, damaging spells, and other harmful effects deal different types of damage. Damage types have no rules of their own, but other rules, such as damage resistance, rely on the types.

The damage types follow, with examples to help a GM assign a damage type to a new effect.

Acid. The corrosive spray of a black dragon's breath and the dissolving enzymes secreted by a black pudding deal acid damage.

Bludgeoning. Blunt force attacks–hammers, falling, constriction, and the like–deal bludgeoning damage.

Cold. The infernal chill radiating from an ice devil's spear and the frigid blast of a white dragon's breath deal cold damage.

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Fire. Red dragons breathe fire, and many spells conjure flames to deal fire damage.

Force. Force is pure magical energy focused into a damaging form. Most effects that deal force damage are spells, including magic missile and spiritual weapon.

Lightning. A lightning bolt spell and a blue dragon's breath deal lightning damage.

Necrotic. Necrotic damage, dealt by certain undead and a spell such as chill touch, withers matter and even the soul.

Piercing. Puncturing and impaling attacks, including spears and monsters' bites, deal piercing damage.

Poison. Venomous stings and the toxic gas of a green dragon's breath deal poison damage.

Psychic. Mental abilities such as a mind flayer's psionic blast deal psychic damage.

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Radiant. Radiant damage, dealt by a cleric's flame strike spell or an angel's smiting weapon, sears the flesh like fire and overloads the spirit with power.

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Slashing. Swords, axes, and monsters' claws deal slashing damage.

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Thunder. A concussive burst of sound, such as the effect of the thunderwave spell, deals thunder damage.

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