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This question already has an answer here:

I'm playing D&D 5e as a DM for about a 3-4 sessions now and the math involved in the Wizard's ability Arcane Ward is a little unclear to me. All of my players just reached level 2 and one of the players is a Wizard who chose The School of Abjuration archetype and he now has the Arcane Ward ability.

Playing by the PHB(p.109) the ability states:

Starting at 2nd level, you can weave magic around yourself for protection. When you cast an abjuration spell of 1st level or higher, you can simultaneously use a strand of the spell's magic to create a magical ward on yourself that lasts until you finish a long rest. The ward has hit points equal to twice your wizard level + your Intelligence modifier.

With his Intelligence modifier (+3) and Wizard level 2 the equation should be:

$$ \begin{align} {Temporary\;HP} &= ( 2 \times {Wizard\;level} ) + {Int\;modifier} \\ &= ( 2 \times 2 ) + 3 \\ &= 4 + 3 \\ &= 7 \end{align} $$

But it can also be:

$$ \begin{align} {Temporary\;HP} &= 2 \times ( {Wizard\;level} + {Int\;modifier} ) \\ &= 2 \times ( 2 + 3 ) \\ &= 2 \times 5 \\ &= 10 \end{align} $$

The text makes it unclear.

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marked as duplicate by PixelMaster, SevenSidedDie dnd-5e Jan 10 at 18:04

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

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    \$\begingroup\$ Related: How are numerical bonuses combined? \$\endgroup\$ – Rykara Jan 10 at 17:32
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    \$\begingroup\$ @Spellcaster Related links are just meant to help people who may be interested in related questions. They aren't meant to imply that they are the same as yours. \$\endgroup\$ – Rubiksmoose Jan 10 at 17:43
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    \$\begingroup\$ @PixelMaster See this FAQ for why your second comment was removed. Thanks! \$\endgroup\$ – SevenSidedDie Jan 10 at 18:03
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7 HP

As Rykara's answer states, the amount of HP the ward has should be 7. The relevant quote from Crawford is:

Arcane Ward—its hit point maximum equals your Intelligence modifier plus twice your wizard level.

But they are not temporary hit points

But it is important to note that these are not Temporary Hit Points.

According to Sage Advice,

An Arcane Ward is not an extension of the wizard who creates it. It is a magical effect with its own hit points. Any temporary hit points, immunities, or resistances that the wizard has don’t apply to the ward.

The ward takes damage first. Any leftover damage is taken by the wizard and goes through the following game elements in order: (1) any relevant damage immunity, (2) any relevant damage resistance, (3) any temporary hit points, and (4) real hit points.

In other words, the ward has 7 of its own Hit Points and the Wizard can still benefit from Temporary Hit Points from another source.

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7 HP

Jeremy Crawford has clarified on Twitter:

Arcane Ward—its hit point maximum equals your Intelligence modifier plus twice your wizard level.

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  • \$\begingroup\$ You are going to want to clarify that OP is making an incorrect assumption in the question: these are not temp HP. Currently your answer seems to be reaffirming that incorrect belief. \$\endgroup\$ – Rubiksmoose Jan 10 at 18:06

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