IN the spirit of SAFE PRACTICE - I am going to try to explain this-
It is EASY to confuse these 2 concentrations - but the key is to remember HOW they are used in clinical practice. Epinephrine is most always a 1mg dose - it just varies with the dilution.
1 mg in 1 ml is ALWAYS used as a SQ medication. It is almost always in a single ml vial, ampoule. This is called 1:1 or 1:1000.
1 mg in 10 ml (of NS) is usually a PRE-FILLED syringe in a boxed container and is given in patient situations that require resuscitation. It is never given except in critical patient situations. This is called 1:10 or 1:10,000.
I think it is more accurate to call it 1:1 (the SQ dose) or 1:10 (the resuscitation dose). It just makes it confusing - and these are some who delight in confusion.
SubCut or SQ - epinephrine is ALWAYS given as a dose strength of:
1 mg (milligram) in 1 ml.
This is commonly called 1:1 epi or 1:1000 epi. I know it can be confusing. This dose is most commonly found in 1 ml vials or rarely in 30 ml MULTI-USE vials. I have never seen this dose in pre-filled syringes.
But the bottom line: LOOK at the medication - IT should note 1 mg in 1 ml.
This dose strength is NEVER DILUTED for administration.
A typical dose of epi given this was is usually:
0.3 mg and will be 0.3 ml
• (sometimes it may be 0.1 mg/0.1 ml or as much as 0.5 mg/0.5 ml in a single dose)
So, what does this mean? To give subQ Epi 1:1 you give the portion of the ml that corresponds to the dose. Each 0.1 ml or 1/10 of the ml is equal to 0.1 mg or 1/10 of a milligram
Use a 1 ml syringe.
Always make it easy on yourself. Use the most accurate syringe for the medication/route that you have available. I find that when giving partial amounts of a single ml - I always find it easier/more accurate to use a small syringe. Draw up the ordered amount of medication.
(Don't even try to administer with a 3 ml syringe - it just gets too confusing! - and can decrease your accuracy!)
DO NOT ATTEMPT to DILUTE this and make it complicated.
This is simple medication administration.
After all you do not want to inject a large quantity (fluid) as SQ administration. Imagine injecting 3 ml as a SQ injection. Ewwww!

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SO good rules for med administration that can save you from disaster:
If it takes multiple dilutions, large numbers of vials, unusual amounts to administer (meaning 5 ml as a SQ injection - or 40 ml as an IV push) the ordered dose - IT IS ALWAYS a GOOD IDEA to STOP.
At this point.
• Clarify the order.
• The 5 rights! Right NOW!
So, the short answer is you DO NOT dilute epi for SQ administration.
But, rather than just noting that - I though it may be useful to know why/how. I hope this was helpful (and not too confusing).
Practice SAFE!