A free stopover on your flight could be the start of an even better vacation

You know all about one-way flights and round-trip flights, and nonstop flights and connecting flights, but do you know about stopover flights?

That’s when you connect through a particular airport, deplane for a day or two, then continue to your destination.

Besides the visit-two-cities-for-the-price-of-one aspect, stopovers let you recover from a long flight by breaking it into two shorter legs.

And some airlines not only let you stop over for free but also include free hotel stays and other perks.

On many airlines, passengers traveling on frequent-flier award tickets can schedule a stopover without forfeiting extra miles or points.

Even if an airline doesn’t have a formal stopover program, it may sell a stopover fare for less than buying a separate onward round-trip ticket.

I recently saw a $721 round-trip fare from Los Angeles to Bangkok, Thailand, on EVA Air, and a three-day stopover in Taipei with an onward journey to Bangkok on the same dates for $954 round-trip.

If you don’t see your airline listed here, check with the airline.

Among the offers:

Air Canada

Stopover: Toronto, Montreal, Vancouver

Maximum stay: Depends on rules associated with the fare

Best way to book: (888) 247-2262 or online at aircanada.com

Cost: Free. More expensive fares may include a free hotel stay,

Air China

Stopover: Beijing, Shanghai and four other major cities on a 144-hour transit visa, and seven other cities on 72-hour transit visa

Maximum stay: 72 or 144 hours, depending on visa

Best way to book: (800) 882-8122 or online at airchina.us

Cost: Free

Copa

Stopover: Panama City

Maximum stay: Check with Copa, which, at press time, was set to announce updates to its stopover program. Maximum stay is seven days.

Best way to book: (800) 359-2672 or online at copaair.com

Cost: Free except for $40 airport departure tax

Emirates

Stopover: Dubai

Maximum stay: Depends on ticket’s fare rules

Best way to book: Book flight with stopover online at emirates.com, then call (800) 777-3999 to book stopover package if desired

Cost: Free

Etihad

Stopover: Abu Dhabi

Maximum stay: Two nights

Best way to book: (877) 690-0767 or online at etihad.com

Cost: Free, and economy fares include a discounted first night hotel rate with the second night free, or two free nights with business class fares.

Fiji Airways

Stopover: Nadi, Fiji

Maximum stay: Three days

Best way to book: (800) 227-4446 or online at fijiairways.com

Cost: Free

Finnair

Stopover: Helsinki, Finland

Maximum stay: Five days

Best way to book: (877) 757-7143 or online at finnair.com

Cost: Free

Hawaiian

Stopover: Honolulu and other Hawaii airports

Maximum stay: No limit as long as there is a scheduled flight in the computer for that date

Best way to book: Online at hawaiianair.com or through a travel agency

Cost: Free for international flights; $60 for domestic stopovers (for example, San Francisco to Honolulu, stopover, Honolulu to Lihue on Kauai)

Iberia

Stopover: Madrid

Maximum stay: Six nights

Best way to book: (800) 772-4642 or online at iberia.com

Cost: Free

Icelandair

Stopover: Reykjavik, Iceland

Maximum stay: Seven days

Best way to book: (800) 223-5500 or online at icelandair.com

Cost: Free

Japan Air Lines

Stopover: Tokyo or Osaka, Japan

Maximum stay: Depends on rules associated with the fare chosen

Best way to book: (800) 525-3663

Cost: Free

Qatar

Stopover city: Doha, Qatar

Maximum stay: 96 hours

Best way to book: Online at qatarairways.com

Cost: Free. Includes a free visa and a hotel stay from $23 per night

SAS

Stopover: Copenhagen

Maximum stay: 12 months

Best way to book: (800) 221-2350 or online at flysas.com

Cost: free

Singapore Airlines

Stopover: Singapore

Maximum stay: Two nights if using the hotel program

Best way to book: Online at singaporeair.com

Cost: $30 to $46 (one-night stay) or $151 (two-night stay including a pass to Universal Studios Singapore and other perks)

Swiss

Stopover: Zurich, Switzerland

Maximum stay: Four days

Best way to book: Online at swiss.com/stopover

Cost: Free

TAP Air Portugal

Stopover: Lisbon or Porto, Portugal

Maximum stay: Five nights

Best way to book: (800) 221-7370 or online at flytap.com or by phone. Download the TAP Stopover App for special perks, such as free wine with dinner

Cost: Free

Turkish

Stopover: Istanbul

Maximum stay: Depends on maximum stay requirement of fare booked

Best way to book: (800) 874-8875) or online at turkishairlines.com

Cost: Free for hotel package stopover; includes one-night hotel stay in Istanbul for economy class or two nights for business class. Non-package stopover in one direction is free, $65 for stopover on both directions.