HomeSearch by dateVacation packagesHotelsFlight dealsCar rentalTravel tips & news
Addis Ababa

$610+ Cheap flights from Frankfurt (FRA) to Addis Ababa (ADD)

This is the cheapest round-trip flight price found by a Cheapflights user in the last 72 hours by searching for a flight departing on 5/9. Fares are subject to change and may not be available on all flights or dates of travel.
FRA — ADD
May 4 — May 111
Sun 5/4
Sun 5/11
1 adult, Economy
We work with more than 300 partners to bring you better travel deals

Find cheap flights from Frankfurt to Addis Ababa with Cheapflights

1. Tell us where you want to go

Enter your travel information like dates, passengers, trip type (one-way or round trip), and preferred cabin class then click “Find deals”

2. Select your favorite providers

We find the providers serving your travel needs. Choose up to four travel providers to compare side-by-side for flights, hotels, or car rentals.

3. Compare prices and book

Review each provider’s pricing and select the best option for you! Book through your favorite provider’s website for a seamless experience.

Cheapflights Tip: The best prices from Frankfurt am Main to Addis Ababa Bole are usually found in March or June, booked 22 days in advance, depart on a Thursday or Tuesday and return on a Saturday

Cheap flight deals from Frankfurt to Addis Ababa

Discover tips and strategies to find the most affordable flight options for your journey from Frankfurt (FRA) to Addis Ababa (ADD). Learn about various techniques such as flexible date searches, comparing prices across and setting up price alerts. Use these methods to find the cheapest flights available for your travel needs. Data last updated April 29, 2025.

Most accurate provider

Mytrip
3 stars

Most trusted provider

Mytrip
3 stars

Round-trip from

$610
(Egyptair)

Popular in

July

Cheapest in

March

Average price

$690

Good round-trip deal

$694 or less

Good one-way deal

$638 or less
Provider with most accurate pricing for Frankfurt am Main-Addis Ababa Bole flight deals.
Search Deals
Provider most trusted by Cheapflights users for Frankfurt am Main-Addis Ababa Bole flights.
Search Deals
From Frankfurt am Main to Addis Ababa Bole
Search Deals
Highest demand for flights based on searches. 11% potential increase in price ($89 potential increase over avg. RT price).
Search Deals
Cheapest flight prices on average. 2% potential price decrease ($20 potential savings vs. average RT price).
Search Deals
Average for round-trip flights in April 2025
Search Deals
Price to beat on a round-trip flight from Frankfurt am Main to Addis Ababa Bole.
Search Deals
Price to beat on a one-way flight from Frankfurt am Main to Addis Ababa Bole.
Search Deals

Find flight deals from Frankfurt to Addis Ababa

Cheapest flights from Frankfurt to Addis Ababa
Explore the most affordable flight options available from Frankfurt to Addis Ababa. Find the lowest fares from popular airlines and budget airlines, with prices last updated on April 29, 2025.

This Egyptair deal was found by Cheapflights users on 4/29. Clicking the “Pick Dates” button in this card will allow you to select your dates and further customize your flight criteria. From there, click “Find deals”, make sure Egyptair is selected, and click “Compare selected” under the list of providers to see comparable flight deals.
Fri 5/93:40 pmFRA - ADD
1 stop10h 30mEgyptair
Mon 5/124:10 amADD - FRA
1 stop11h 00mEgyptair
Deal found 4/29$610
This Turkish Airlines deal was found by Cheapflights users on 4/29. Clicking the “Pick Dates” button in this card will allow you to select your dates and further customize your flight criteria. From there, click “Find deals”, make sure Turkish Airlines is selected, and click “Compare selected” under the list of providers to see comparable flight deals.
Mon 10/276:20 pmFRA - ADD
1 stop27h 25mTurkish Airlines
Fri 11/1412:45 amADD - FRA
1 stop15h 15mTurkish Airlines
Deal found 4/29$618
This Mytrip deal was found by Cheapflights users on 4/29. Clicking the “Pick Dates” button in this card will allow you to select your dates and further customize your flight criteria. From there, click “Find deals”, make sure Mytrip is selected, and click “Compare selected” under the list of providers to see comparable flight deals.
Sat 5/32:45 pmFRA - ADD
3 stops27h 15mMultiple Airlines
Mon 6/210:05 pmADD - FRA
2 stops15h 30mMultiple Airlines
Deal found 4/29$688
This Ethiopian Air deal was found by Cheapflights users on 4/29. Clicking the “Pick Dates” button in this card will allow you to select your dates and further customize your flight criteria. From there, click “Find deals”, make sure Ethiopian Air is selected, and click “Compare selected” under the list of providers to see comparable flight deals.
Mon 9/110:05 pmFRA - ADD
Nonstop6h 50mEthiopian Air
Mon 9/2912:05 amADD - FRA
Nonstop7h 20mEthiopian Air
Deal found 4/29$731
This Orbitz deal was found by Cheapflights users on 4/29. Clicking the “Pick Dates” button in this card will allow you to select your dates and further customize your flight criteria. From there, click “Find deals”, make sure Orbitz is selected, and click “Compare selected” under the list of providers to see comparable flight deals.
Thu 5/2910:05 pmFRA - ADD
Nonstop6h 50mLufthansa
Wed 6/412:05 amADD - FRA
Nonstop7h 20mLufthansa
Deal found 4/29$752
This British Airways deal was found by Cheapflights users on 4/29. Clicking the “Pick Dates” button in this card will allow you to select your dates and further customize your flight criteria. From there, click “Find deals”, make sure British Airways is selected, and click “Compare selected” under the list of providers to see comparable flight deals.
Tue 5/203:55 pmFRA - ADD
2 stops31h 15mBritish Airways
Mon 6/161:50 amADD - FRA
2 stops21h 35mBritish Airways
Deal found 4/29$784
This FlightHub deal was found by Cheapflights users on 4/29. Clicking the “Pick Dates” button in this card will allow you to select your dates and further customize your flight criteria. From there, click “Find deals”, make sure FlightHub is selected, and click “Compare selected” under the list of providers to see comparable flight deals.
Fri 5/96:15 pmFRA - ADD
1 stop10h 25mITA Airways
Sun 5/1112:15 amADD - FRA
1 stop11h 35mITA Airways
Deal found 4/29$868
This Booking.com deal was found by Cheapflights users on 4/29. Clicking the “Pick Dates” button in this card will allow you to select your dates and further customize your flight criteria. From there, click “Find deals”, make sure Booking.com is selected, and click “Compare selected” under the list of providers to see comparable flight deals.
Thu 5/2910:55 amFRA - ADD
2 stops17h 50mAir Europa
Wed 6/412:05 amADD - FRA
2 stops18h 45mAir Europa
Deal found 4/29$951
This SAUDIA deal was found by Cheapflights users on 4/29. Clicking the “Pick Dates” button in this card will allow you to select your dates and further customize your flight criteria. From there, click “Find deals”, make sure SAUDIA is selected, and click “Compare selected” under the list of providers to see comparable flight deals.
Thu 5/154:15 pmFRA - ADD
1 stop11h 05mSAUDIA
Mon 5/1910:35 pmADD - FRA
1 stop89h 10mSAUDIA
Deal found 4/29$964
This Qatar Airways deal was found by Cheapflights users on 4/29. Clicking the “Pick Dates” button in this card will allow you to select your dates and further customize your flight criteria. From there, click “Find deals”, make sure Qatar Airways is selected, and click “Compare selected” under the list of providers to see comparable flight deals.
Mon 7/149:35 amFRA - ADD
1 stop13h 45mQatar Airways
Sat 8/91:50 amADD - FRA
1 stop18h 05mQatar Airways
Deal found 4/29$1,135
This Austrian Airlines deal was found by Cheapflights users on 4/29. Clicking the “Pick Dates” button in this card will allow you to select your dates and further customize your flight criteria. From there, click “Find deals”, make sure Austrian Airlines is selected, and click “Compare selected” under the list of providers to see comparable flight deals.
Sat 7/123:50 pmFRA - ADD
1 stop12h 35mAustrian Airlines
Thu 7/3112:35 amADD - FRA
1 stop12h 25mAustrian Airlines
Deal found 4/29$1,269
This United Airlines deal was found by Cheapflights users on 4/28. Clicking the “Pick Dates” button in this card will allow you to select your dates and further customize your flight criteria. From there, click “Find deals”, make sure United Airlines is selected, and click “Compare selected” under the list of providers to see comparable flight deals.
Wed 4/3010:00 amFRA - ADD
3 stops34h 10mUnited Airlines
Sun 5/410:50 pmADD - FRA
3 stops34h 20mUnited Airlines
Deal found 4/28$14,355

Cheapflights Fare Finder

Customize your flight search to find flights from Frankfurt to Addis Ababa that fit within your specific budget. Explore options based on user searches and filter the results based on your desired price range. Find flights that match your budget for a cost-effective journey. Over the last 7 days, Cheapflights users made 2,558,603 searches. Data last updated April 29, 2025.
Use the filters below to find and compare flights from Frankfurt am Main Airport to Addis Ababa that are best for you.

Fly from

Frankfurt

Fly to

Addis Ababa

Route

Depart

Return

Price

Frankfurt am MainAddis Ababa

FRA - ADD

FRAADD

Frankfurt am Main

Fri 5/9

3:40 pm-3:10 am

1 stop10h 30m

Addis Ababa Bole

Mon 5/12

4:10 am-2:10 pm

1 stop11h 00m

$610

Frankfurt am MainAddis Ababa

FRA - ADD

FRAADD

Frankfurt am Main

Sat 5/10

6:55 pm-11:45 pm

1 stop27h 50m

Addis Ababa Bole

Sat 5/31

12:45 am-1:25 pm

1 stop13h 40m

$623

Frankfurt am MainAddis Ababa

FRA - ADD

FRAADD

Frankfurt am Main

Thu 5/29

9:00 pm-4:45 am

2 stops30h 45m

Addis Ababa Bole

Wed 6/4

3:35 am-2:45 pm

1 stop12h 10m

$719

Frankfurt am MainAddis Ababa

FRA - ADD

FRAADD

Frankfurt am Main

Mon 9/1

10:05 pm-5:55 am

Nonstop6h 50m

Addis Ababa Bole

Mon 9/29

12:05 am-6:25 am

Nonstop7h 20m

$731

Frankfurt am MainAddis Ababa

FRA - ADD

FRAADD

Frankfurt am Main

Thu 5/29

10:05 pm-5:55 am

Nonstop6h 50m

Addis Ababa Bole

Wed 6/4

12:05 am-6:25 am

Nonstop7h 20m

$752

Frankfurt am MainAddis Ababa

FRA - ADD

FRAADD

Frankfurt am Main

Tue 5/20

3:55 pm-12:10 am

2 stops31h 15m

Addis Ababa Bole

Mon 6/16

1:50 am-10:25 pm

2 stops21h 35m

$784

Frankfurt am MainAddis Ababa

FRA - ADD

FRAADD

Frankfurt am Main

Fri 5/9

6:15 pm-5:40 am

1 stop10h 25m

Addis Ababa Bole

Sun 5/11

12:15 am-10:50 am

1 stop11h 35m

$868

Frankfurt am MainAddis Ababa

FRA - ADD

FRAADD

Frankfurt am Main

Thu 5/29

10:55 am-5:45 am

2 stops17h 50m

Addis Ababa Bole

Wed 6/4

12:05 am-5:50 pm

2 stops18h 45m

$951

Frankfurt am MainAddis Ababa

FRA - ADD

FRAADD

Frankfurt am Main

Thu 5/15

4:15 pm-4:20 am

1 stop11h 05m

Addis Ababa Bole

Mon 5/19

10:35 pm-2:45 pm

1 stop89h 10m

$964

Frankfurt am MainAddis Ababa

FRA - ADD

FRAADD

Frankfurt am Main

Mon 7/14

9:35 am-12:20 am

1 stop13h 45m

Addis Ababa Bole

Sat 8/9

1:50 am-6:55 pm

1 stop18h 05m

$1,135

Flights are sorted by cheapest round-trip flights first.

Deals found on 4/29

Showing 1-10 of 13 results
1
2

Compare providers for flights from Frankfurt to Addis Ababa

Provider information is updated monthly. Please note that these providers often have deals for this flight, but the availability may vary on a day-by-day basis on Cheapflights.
Use the table below to compare price accuracy, trust ratings, and cancellation policies for each provider offering flight deals from Frankfurt to Addis Ababa in April.
ProviderPrice AccuracyTrust Score*
eDreamsPrice Accuracy3 starsTrust Score*3 stars
FlightHubPrice Accuracy3 starsTrust Score*2 stars
MytripPrice Accuracy3 starsTrust Score*3 stars
FlightnetworkPrice Accuracy-Trust Score*3 stars
GotogatePrice Accuracy3 starsTrust Score*2 stars
Trip.comPrice Accuracy1 starTrust Score*3 stars

*The Trust Score is based on feedback from users after their booking experience. It measures overall satisfaction, helping us identify issues like hidden fees, problems during the ticketing process, and the quality of customer service. This score is our best indicator of the provider's quality and reliability.

  • Most accurate provider: When it comes to deals on Frankfurt am Main Airport-Addis Ababa flights, users find the pricing of Mytrip to be most consistent on Cheapflights vs. Mytrip Users can find the same prices on Frankfurt am Main Airport-Addis Ababa flight deals on Cheapflights vs. Mytrip >95% of the time. Price accuracy is based on data collected from Frankfurt am Main Airport-Addis Ababa flight searches over the past month and is updated monthly.
  • Most trusted provider: When it comes to deals on Frankfurt am Main Airport-Addis Ababa flights, Cheapflights users trust Mytrip the most. Mytrip has received a user feedback score of 3 out of 3 stars (3 being the best), meaning they have been trusted the most by Cheapflights users looking for Frankfurt am Main Airport-Addis Ababa flight deals. Provider user feedback score is based on Cheapflights searches over the past month and is updated monthly.

Best time to book a flight from Frankfurt to Addis Ababa

Have a flexible travel schedule? Discover the best time to fly to Addis Ababa from Frankfurt with our price prediction graph.
Estimated round-trip price
Rates are based on past data. Find the cheapest month and day to book your flight based on your travel requirements, then search for cheap deals.

Cheapflights Insights

Everything you need to know about your flight from Frankfurt am Main Airport to Addis Ababa

How far ahead should I book a flight from Frankfurt am Main Airport to Addis Ababa?

Use this chart to determine the optimal time to book a round-trip flight from Frankfurt to Addis Ababa. Price data was last updated on April 25, 2025.

The price you pay for your flight from Frankfurt am Main Airport to Addis Ababa may vary depending on when you book. For the best chance of a lower fare, look to book 8 days in advance of your trip. Fares are likely to increase a fortnight or so before your departure date.

What is the cheapest month to book a flight from Frankfurt am Main Airport to Addis Ababa?

Currently, October is the cheapest month in which you can book a flight from Frankfurt am Main Airport to Addis Ababa (average of $988). Flying from Frankfurt am Main Airport to Addis Ababa in June is currently the most expensive (average of $1,615). There are several factors that can impact the price of a flight, so comparing airlines, departure airports and flight times can provide users with more options.

What is the cheapest time of day to fly from FRA to ADD?

Find hourly flight availability from Frankfurt to Addis Ababa. Discover flight options and departure times throughout the day, allowing you to choose a departure time that suits your schedule. Data last updated April 29, 2025.

It’s typically best to fly out from Frankfurt am Main Airport to Addis Ababa at noon. Doing so could potentially save you 36% on the flight price compared to flying in the afternoon, which is usually more expensive.

Weekly flight availability from Frankfurt am Main Airport to Addis Ababa

Explore weekly flight availability from Frankfurt to Addis Ababa. Discover flights operating on different days of the week, giving you the flexibility to choose a travel day that best fits your plans. Compare info to find the most convenient option for your journey. Data last updated April 29, 2025.

The most flights from FRA to ADD are scheduled on a Monday (5 on average). You will have fewer flight options on Monday, which is when the least amount of flights are scheduled (5 on average).

Rainfall in Addis Ababa by month

Plan your trip to Addis Ababa by taking into account the average rainfall totals by month.

In terms of precipitation, rainfall in Addis Ababa ranges from 0.4 - 11.0 inches per month. August is typically the wettest month, when rainfall can reach 11.0 in. January is typically the driest time to visit Addis Ababa when rainfall is around 0.4 in.

Temperature in Addis Ababa by month

Plan your trip to Addis Ababa by taking into account the average temperature totals by month.

If weather is an important factor for your trip to Addis Ababa, use this chart to help with planning. For those seeking warmer temperatures, May is the ideal time of year to visit, when temperatures reach an average of 64.4 F. Travelers looking to avoid the cold should look outside of July, when temperatures are typically at their lowest (around 59.0 F).

Reviews of airlines servicing Addis Ababa

Get insights into the airlines that provide service to Addis Ababa. Read reviews, discover amenities, and learn about the overall travel experience offered by airlines. Use this information to make informed decisions when choosing an airline for your flight to Addis Ababa. Reviews last updated April 29, 2025.
See what other customers who have flown with Austrian Airlines, Qatar Airways and SAUDIA from Frankfurt am Main to Addis Ababa have to say. Users can see the overall rating for each airline as well as how each is rated in terms of entertainment options, comfort, food, crew/service, and boarding process.
Austrian Airlines
7.6
Good
780 reviews

Food

6.7

Overall

7.6

Comfort

7.3

Boarding

7.6

Crew

8.1

Entertainment

6.7

Reviews

1 / 20
8.0
Excellent

Ely,Mar 2025

VIE - PMI

Luggage at destination was not split into priorities. Had business and only got my bag after 20 minutes, almost towards the end and I was in a rush, so the "priority" was completely ignored.
Austrian Airlines
7.6
Good
780 reviews
Austrian Airlines
7.6
Good
780 reviews

Food

6.7

Overall

7.6

Comfort

7.3

Boarding

7.6

Crew

8.1

Entertainment

6.7

Reviews

1 / 20
8.0
Excellent

Ely,Mar 2025

VIE - PMI

Luggage at destination was not split into priorities. Had business and only got my bag after 20 minutes, almost towards the end and I was in a rush, so the "priority" was completely ignored.
Qatar Airways
7.4
Good
3,563 reviews
Austrian Airlines
7.6
Good
780 reviews

Food

6.7

Overall

7.6

Comfort

7.3

Boarding

7.6

Crew

8.1

Entertainment

6.7

Reviews

1 / 20
8.0
Excellent

Ely,Mar 2025

VIE - PMI

Luggage at destination was not split into priorities. Had business and only got my bag after 20 minutes, almost towards the end and I was in a rush, so the "priority" was completely ignored.
SAUDIA
7.4
Good
611 reviews
Austrian Airlines
7.6
Good
780 reviews

Food

6.7

Overall

7.6

Comfort

7.3

Boarding

7.6

Crew

8.1

Entertainment

6.7

Reviews

1 / 20
8.0
Excellent

Ely,Mar 2025

VIE - PMI

Luggage at destination was not split into priorities. Had business and only got my bag after 20 minutes, almost towards the end and I was in a rush, so the "priority" was completely ignored.
United Airlines
7.4
Good
8,696 reviews
Austrian Airlines
7.6
Good
780 reviews

Food

6.7

Overall

7.6

Comfort

7.3

Boarding

7.6

Crew

8.1

Entertainment

6.7

Reviews

1 / 20
8.0
Excellent

Ely,Mar 2025

VIE - PMI

Luggage at destination was not split into priorities. Had business and only got my bag after 20 minutes, almost towards the end and I was in a rush, so the "priority" was completely ignored.
Turkish Airlines
7.3
Good
3,788 reviews
Austrian Airlines
7.6
Good
780 reviews

Food

6.7

Overall

7.6

Comfort

7.3

Boarding

7.6

Crew

8.1

Entertainment

6.7

Reviews

1 / 20
8.0
Excellent

Ely,Mar 2025

VIE - PMI

Luggage at destination was not split into priorities. Had business and only got my bag after 20 minutes, almost towards the end and I was in a rush, so the "priority" was completely ignored.

Related info for your journey

Find useful and relevant information for your journey from Frankfurt to Addis Ababa. Access travel guides, tips, and recommendations to enhance your travel experience. Get information about local attractions, weather, transportation options, and more.

  • What airport do you fly into for flights to Addis Ababa from Frankfurt am Main?

    Most people fly into Addis Ababa Bole (ADD) if they book a flight to Addis Ababa from Frankfurt am Main. On average, Bole has 5 inbound flights from Frankfurt am Main per day from 4 airlines. Addis Ababa Bole is conveniently located just 4.8 mi from Addis Ababa’s city center.

  • What are the cheapest airlines flying from Frankfurt am Main Airport to Addis Ababa round-trip?

    Our cheapest airline available from Frankfurt am Main Airport to Addis Ababa is Egyptair. Our recent data shows that you can find tickets from as low as $610 on this airline. Additional options worth looking into are Turkish Airlines and Ethiopian Air, starting at $623 and $731 round-trip. Egyptair is priced at 15% lower than the current average price of a flight leaving 3 months from now.

  • What are the most reliable airlines from Frankfurt am Main Airport to Addis Ababa?

    The top 3 most reliable airlines when flying from Frankfurt am Main Airport to Addis Ababa are ANA (93%), United Airlines (93%) and TAP AIR PORTUGAL (93%).

  • What are the cheapest flights from Frankfurt am Main Airport to Addis Ababa?

    Looking for the cheapest flight from Frankfurt am Main Airport to Addis Ababa? While on average our users pay $936, our data indicates the cheapest price to be $576. The most popular route (Frankfurt am Main - Addis Ababa Bole), is priced around $730.

  • Can I find deals for flights from Frankfurt to Addis Ababa that include hotel bookings?

    Yes. In addition to deals on Frankfurt to Addis Ababa flights, Cheapflights offers vacation packages that include both flights and hotel.

  • How can I find direct flights from Frankfurt to Addis Ababa?

    After entering your origin and destination, apply the non-stop filter on the search result page to find direct flights from Frankfurt to Addis Ababa.

  • Can I find deals for business class flights from Frankfurt to Addis Ababa?

    Yes. Cheapflights offers flight deals from Frankfurt to Addis Ababa by cabin class. In addition to browsing deals, you can also filter by cabin class on the search results page after making a search.

  • What is the cheapest month to book a flight from Frankfurt am Main Airport to Addis Ababa?

    Currently, October is the cheapest month in which you can book a flight from Frankfurt am Main Airport to Addis Ababa (average of $988). Flying from Frankfurt am Main Airport to Addis Ababa in June is currently the most expensive (average of $1,615). There are several factors that can impact the price of a flight, so comparing airlines, departure airports and flight times can provide users with more options.

See more FAQs

Browse thousands of different options on Cheapflights for your next trip

Toggle through the tabs below to find thousands of options on Cheapflights for your next trip.

Other flights to Addis Ababa

Explore flights to Addis Ababa departing from other origins. Flights are based on user searches made on Cheapflights and were last updated on April 29, 2025.
John F Kennedy Intl to Addis Ababa flights
Atlanta to Addis Ababa flights
O'Hare Intl to Addis Ababa flights
Dulles Intl to Addis Ababa flights
Newark to Addis Ababa flights
Addis Ababa to Dessie flights
Addis Ababa to Bahir Dar flights
Addis Ababa to Arba Minch flights
Addis Ababa to Lalībela flights
Addis Ababa to Awassa flights
Addis Ababa to Mekele flights
Addis Ababa to Dire Dawa flights
Addis Ababa to Jeddah flights
Addis Ababa to Jeddah flights
Addis Ababa to Bahir Dar flights
Addis Ababa to Riyadh flights
Addis Ababa to Dire Dawa flights
Addis Ababa to Lalībela flights
Addis Ababa to Arba Minch flights
Addis Ababa to Cairo flights
Addis Ababa to Riyadh flights
Addis Ababa to Cairo flights
Addis Ababa to Mekele flights

Top 4 airlines flying from Frankfurt to Addis Ababa

Discover the top 4 airlines that operate flights from Frankfurt to Addis Ababa. Compare their services, reliability, and customer satisfaction ratings to choose the airline that best suits your travel preferences and needs. Over the last 7 days, Cheapflights users made 2,558,603 searches. Data last updated April 29, 2025.
AirlineCheapestAverageFlexibilityOn-time
EgyptairCheapest$522Average$627FlexibilityNo cancel feeOn-timeN/A
Turkish AirlinesCheapest$558Average$618FlexibilityNo cancel feeOn-time77%
Ethiopian AirCheapest$642Average$751FlexibilityNo cancel feeOn-time72%
LufthansaCheapest$717Average$827FlexibilityNo cancel feeOn-time76%

100% Free

Cheapflights is completely free to use, so you can start saving the moment you arrive.

Book with Flexibility

Our users can plan ahead with confidence and find flights with no change fees

Travel Smart

Millions of people come to us for their flight needs every year. We help make travel planning easy by providing useful insights and data-driven graphs that can inform your decisions.