Thermory
Thermory is a global leader in thermally enhanced wood and long-lasting saunas kits.
Thermally modified timber is the key strength at Thermory. With our exclusive,
state of-the-art technology and years of expertise, they know exactly how to bring out the best in wood. Thermally modified wood is natural – its
properties are enhanced using just heat and steam. This chemical-free process
results in an environmentally friendly and aesthetically pleasing material that’s
significantly more durable and stable than conventional timber.
As well as offering these practical benefits, Thermory’s thermal modification treatment also creates dynamic visual effects, with the wood taking on an appealing darker brown shade. The intensity of the color depends on the wood type and the duration and temperature of the modification process.
The highest temperature of medium thermal modification is 374 °F and intense
modification 410 °F. This gives you the opportunity to choose between lighter and darker materials to suit your desired color palette.
Thermally modified timber is suitable for interior and exterior use in both homes and public spaces.
1X4 Black Thermo-Spruce STS4 T&G Wall Cladding – Brushed & Waxed Black Sauna Wood by Thermory
$4.27 – $251.00The Bold New Statement in Sauna Design
Introducing Black Thermo-Spruce – the dramatic, sophisticated sauna wood that’s revolutionizing modern sauna aesthetics. This isn’t paint or stain; it’s the natural beauty of spruce transformed through Thermory’s intensive thermal modification process, creating a rich, deep black that’s as durable as it is stunning.
Wire-brushed to perfection, each board reveals the natural grain patterns that make every installation unique. The textured surface doesn’t just look incredible – it feels amazing under your fingertips, adding a tactile dimension to your sauna experience. Finally, a true black sauna wood at a price that makes sense.
5/4 x 4 SHP Alder Bench, Backrest, and Skirt Sauna Wood
$4.32 – $172.65Alder 1×4 SHP Bench material is the classic choice for a timeless sauna. With subtle yet appealing tone and aroma, Alder is the perfect natural sauna material with moisture wicking properties. Recommended Uses: Sauna benches, backrests, and skirting.
1×4 Bench Boards are an easy and low-cost way to build a premium sauna bench framed with standard 2x4s and decked with these .83″ thick boards horizontally or vertically. See below for our framing suggestion.
Thermory 1×4 SHP Alder Bench, Backrest, and Skirt Sauna Wood
$3.52 – $176.13Alder 1×4 SHP Bench material is the classic choice for a timeless sauna. With subtle yet appealing tone and aroma, Alder is the perfect natural sauna material with moisture wicking properties. Recommended Uses: Sauna benches, backrests, and skirting.
1×4 Bench Boards are an easy and low-cost way to build a premium sauna bench framed with standard 2x4s and decked with these .83″ thick boards horizontally or vertically. See below for our framing suggestion.
1X4 Thermo-Aspen STS4 T&G Wall Cladding – Thermally Modified Sauna Wood by Thermory
$2.85 – $170.67Thermally Modified Aspen (TASP) is an elegant wall and ceiling cladding for saunas that has been meticulously processed using only heat and steam by Thermory, the global leader in Thermal Modification. The result is a darkened, smooth wood that won’t shrink, warp, cup, or rot when properly installed. Choose this profile for a classic sauna look that’s more refined than typical North American saunas.
Working with Tongue and Groove STS4 is a delight for contractors and DIY Sauna Builders alike. We’re not exagerating that every builder we work with has found the quality and consistency to be truly remarkable. At Sauna Marketplace, we make it easy with matching benches, backrests, bench skirts, vent hatches, floor grids, and more.
Actual wall coverage is 3.1″ to 3.2″ depending on installation.
Thermo-Magnolia Wide Sauna Bench Board 5/4×8 SHP
$13.62 – $533.90These extra-wide bench boards in exquisite thermo-magnolia will add a touch of comfort while enhancing the look of your home. The rich, dark shade is achieved by thermal modification giving magnolia an exclusive, stately finish. Create your dream sauna or high-end sauna space.
If you want to something a little ‘extra’, we think this is the most premium sauna bench material on the market. Magnolia has attractive grain patterns, low thermal conductivity, and resists warping and cupping making it perfect as a wide-plank premium sauna bench material that won’t splinter. This is also the widest plank sauna bench material available in North America, coming in at 7.3″ of actual width.
Dark Thermo-Alder 5/4×4 SHP Bench, Backrest, and Skirt Sauna Wood – Intense Modification by Thermory
$4.84 – $170.37Dark Thermo-Alder 5/4 SHP Bench material is a perfect choice for sturdy, warm-tone benches that are smooth to the touch. This dark-tone thermo-aspen is more brown and woodsy looking than thermo-aspen. Ideal for a more traditional cabin-sauna or cottage feel.
5/4×4 Bench Boards are an easy and low-cost way to build a premium sauna bench framed with standard 2x4s and decked with these 1.1″ thick boards horizontally or vertically. See below for our framing suggestion.
Dark Thermo-Alder Wall Paneling 1×5 STS4 – Intense Thermal Modification Sauna Wood by Thermory
$4.73 – $278.12Thermal modification darkens wood, and intense thermal modification darkens wood even more. It also takes the benefits of thermal modification to the next level.
Wide plank 1×5 thermo-alder is an exceptional sauna wall material that can be installed vertically or horizontally. The natural brown tone provides a classic, upscale sauna look. Thermally modified alder is one of the best-performing sauna woods, with a warm tone, unbeatable performance, and timeless appeal. The minimal expansion and contraction of Dark Thermo-Alder allows for tight, seamless transitions without molding.
Thermo-Spruce Sauna Bench and Floor Wood – 5/4 SHP Sauna Wood By Thermory
$2.95 – $173.46One of our missions at Sauna Marketplace is to make it more affordable to build a DIY sauna without compromise. Sauna bench wood has always been a barrier, but this 5/4 SHP Bench profile from Thermory makes it easier than ever.
Intense natural modification using heat and steam alters this Nordic Spruce at a cellular level, resulting in a more durable and healthy choice than Western Red Cedar at a fraction of the price. Unlike WRC, this Thermo-Spruce won’t warp, expand, contract, or cup.
Recommended Uses: Sauna benches, backrests, flooring, and skirting. These 1.0″ thick sauna bench boards are thick enough to build the frame, but we recommend using standard 2x4s for that. See detail below.
1X4 Thermo-Spruce STS4 T&G Wall Cladding – Thermally Modified Sauna Wood by Thermory
$1.73 – $101.72Thermo-Spruce 1×4 by Thermory is the most affordable way to achieve beautiful thermally modified wood walls in your sauna. Popular in Finland for it’s thermal performance, Nordic Spruce is also a sustainable choice. We love the rustic look and unique, tight knots that look like wings. Thermo-Spruce gives a pleasant, mild aroma with far lower VOC content than Western Red Cedar. Natural thermal modification changes the wood at a cellular level to resist rot, decay, warping, and cupping.
Actual wall coverage is 3.1″ to 3.2″, depending on installation. Thermo-Spruce pairs well with Thermo-Aspen benches.
Thermory 5/4×4 SHP Thermo-Alder Bench, Backrest, and Skirt Sauna Wood
$5.92 – $232.06Thermo-Alder 5/4 SHP Bench material is a great choice for sturdy, warm-tone benches that are smooth to the touch. This mid-tone thermo-aspen is more brown and woodsy looking than thermo-aspen. Ideal for a more traditional cabin-sauna or cottage feel (an even darker, intensely modified thermo-alder is also available).
5/4×4 Bench Boards are an easy and low-cost way to build a premium sauna bench framed with standard 2x4s and decked with these 1.1″ thick boards horizontally or vertically. See below for our framing suggestion.
Thermory 1×4 SHP Thermo-Alder Bench, Backrest, and Skirt Sauna Wood
$4.96 – $243.04Thermo-Alder 1×4 SHP Bench material is a popular choice for sauna benches, backrests, and skirting. This mid-tone is more brown and woodsy looking than thermo-aspen. Great for a more traditional cabin-sauna or cottage feel.
1×4 Bench Boards are an easy and low-cost way to build a premium sauna bench framed with standard 2x4s and decked with these .83″ thick boards horizontally or vertically. See below for our framing suggestion.
Thermo-Alder Wall Paneling 1×5 STS4 – Sauna Wall and Ceiling Wood By Thermory
$3.56 – $209.00Wide plank 1×5 thermo-alder is an exceptional sauna wall material that can be installed vertically or horizontally. The natural brown tone provides a classic, upscale sauna look. Thermally modified alder is one of the best-performing sauna woods, with a warm tone, unbeatable performance, and timeless appeal. The minimal expansion and contraction of Thermo-Alder allows for tight, seamless transitions without molding.
Thermo-Alder Wall Paneling 1×4 STS4 (JEM) – Sauna Wall and Ceiling Wood By Thermory
$3.56 – $209.001×4 STS4 JEM in premium Thermo-Alder is unique in our sauna wood catalog, with tongue and groove ends. That means you don’t need full-length boards and can create stunning visual effects with staggard seams that are perfect every time. Thermally modified alder is one of the best-performing woods, with a warm tone, and a favorite among high-end sauna builders and manufacturers.
Alder Wall To Wall Flat T Transition Trim
$34.80Need longer wall cladding boards in alder than those available by Thermory? We make those transitions easy with this T moulding to avoid gaps with a professional look. Common on walls and ceilings in commercial saunas.
Note: These will arrive directly from Thermory USA in bundles of two in 7′ and 8′ lengths.
Alder Moulding 1×1 SI Sauna Ceiling Trim By Thermory
$2.00 – $64.00Alder 1×1 SI makes sauna building easier than ever. These 0.59″x 0.71″ are ideal for concealing the gap and giving a professional finish to any wall-to-ceiling transition. Make it easy, make it beautiful with Thermory 1×1 ceiling mouldings in Alder.
Note: These will arrive directly from Thermory USA in bundles of four in 7′ and 8′ lengths.
Alder Moulding 1×1 SHP Sauna Trim, Floor, and Bench Wood By Thermory
$2.00 – $160.00Alder 1×1 SHP is a versatile sauna material for trim, benches, internal corner molding, and sauna floors. Cover any inward-facing corners in your sauna with this elegant moulding profile in natural alder. Alder is a hardy and water-repellent wood that doesn’t overheat, with a beautiful reddish tone and a pleasant texture.
These 0.83″ thick boards are ideal for creative projects and making your sauna design truly unique. Note: These can only be purchased in bundles of 10 in 7′ and 8′ lengths.
Alder 5/4×3 STEP Wall Cladding – Sauna Wood by Thermory
$3.72 – $223.97Step up your game and build the sauna of your dreams with Alder STEP Cladding by Thermory. The broad, square grooves create a striking shadow effect, adding depth and intrigue to any space. It’s our go-to for vertical wall cladding in any high-end sauna build.
Alder is a popular and timeless sauna wood with natural water repelling properties. It’s a medium tone with reddish tints and a subtle honey-like aroma. At Sauna Marketplace, we make it easy to build an Alder sauna with matching benches, backrests, bench skirts, vent hatches, floor grids, and more.
The actual wall coverage is 2.2″, which completes the step.
1X5 Brushed Black Alder STS4 Wall Cladding – Sauna Wood by Thermory
$4.56 – $268.00Looking for a smooth, black sauna wood with a professional finish? The wire-brushed black wax alder by Thermory is a perfect choice for a durable finish. Whether contrasting with woods like thermo-aspen or going all dark for the ancient ‘smoke sauna’ look this STS4 1×5 is an ideal choice for a wide plank wall and ceiling cladding. Actual wall coverage is 4.4″.
Note: Brushed black alder does NOT have the burnt Shou Sugi Ban (yakisugi) look as other websites incorrectly show. Please ask us about ‘Thermory Ignite’ for that.
1X5 Alder STS4 Wall Cladding – Natural Sauna Wood by Thermory
$3.83 – $230.20Wide plank alder is a solid choice for any traditional Finnish sauna. Natural alder is naturally resistant to water and a favorite among sauna builders who prefer a timeless, classic look with mild aroma.
Actual wall coverage is 4.3″.
1X4 Alder STS4 T&G Wall Cladding – Sauna Wood by Thermory
$2.96 – $177.62Coveted in Finland and worldwide, European alder brings timeless elegence to your sauna with its distinctive reddish tone and inviting texture. This premium 1×4 natural profile offers excellent thermal properties (0.12 W/m·K) and sound absorption, creating the ideal surroundings and conditions for healing heat. Completely untreated and E1 certified for ultra-low emissions, this alder tongue and groove cladding maintains its warm, honey-like fragrance while providing the perfect balance of durability and comfort. Choose this medium-toned Estonian-crafted wood for an authentic sauna experience that harmonizes tradition with European quality standards.
1×4 STS4 By Thermory might just be nature’s perfect sauna companion.
Thermory 5/4 SHP Thermo-Aspen Sauna Bench and Floor Wood
$4.26 – $170.67Thermory Thermo-Aspen 5/4 (previously called 2×4) SHP Bench material is the perfect smooth, cool timber to feel against bare skin. Because it doesn’t secrete resin, splinter or overheat, aspen makes for an ideal sauna material. The color of thermally modified aspen is an attractive golden brown. Thermally modified wood resists rotting, expansion, contraction, warping, and cupping. Recommended Uses: Sauna benches, backrests, flooring, and skirting.
These 1.1″ thick sauna bench boards are thick enough to build the frame, but we recommend using standard 2x4s for that. See detail below.
Thermory 1×4 SHP Thermo-Aspen Bench, Backrest, and Skirt Sauna Wood
$3.49 – $174.47Thermory Thermo-Aspen 1×4 SHP Bench material is the perfect smooth, cool timber to feel against bare skin. Because it doesn’t secrete resin, splinter or overheat, aspen makes for an ideal sauna material. The color of thermally modified aspen is an attractive golden brown. Thermally modified wood resists rotting, expansion, contraction, warping, and cupping. Recommended Uses: Sauna benches, backrests, and skirting.
1×4 Bench Boards are an easy and low-cost way to build a premium sauna bench framed with standard 2x4s and decked with these .83″ thick boards either horizontally or vertically. See below for our framing suggestion.
Thermory Accessory Kit
Like everything they do, the Thermory Sauna Accessory Kit is modern, stylish, precise, and built to last. Comes with a Bucket, Ladle, Thermometer-Hygrometer, and Sand Timer.
Black Aspen Indoor Sauna Windows by Thermory
$295.00 – $495.00Indoor windows from Thermory are stylish, versatile, modern. Ideal for any commercial sauna or modern home. These tall transom windows bring a touch of contemporary class to your
interior spaces with Thermory quality. Practical and easy on the eye in equal measure, the windows are available in two size options with black aspen frames and single-glazed tempered gray glass that offers shade and privacy. They are also suitable for use in damp environments, making them perfect for adding visual appeal to a home sauna or spa.
Thermo-Aspen 1×4 VIRE Wall Cladding – Sauna Wood by Thermory
$4.65 – $279.96Add some life to your sauna with Thermory Vire 1×4, a unique contoured cladding for sauna walls and ceilings. This is also a favorite for adjascent walls the sauna, or for building a hidden door into a wood wall!
Thermo-Aspen is an elegant wall and ceiling cladding for saunas that has been meticulously processed using only heat and steam by Thermory, the global leader in Thermal Modification. The result is a darkened, smooth wood that won’t shrink, warp, cup, or rot when properly installed. Choose this profile for a warm, modern sauna that’s design forward.
At Sauna Marketplace, we make it easy with matching benches, backrests, bench skirts, vent hatches, floor grids, and more.
Actual wall coverage is 3.1″.
Thermo-Aspen 1×4 KYTE Wall Cladding – Motion Panels by Thermory
$3.72 – $223.97Step up your game and build the sauna of your dreams with Kyte Cladding by Thermory. The subtle bump out is easy to work with, but adds intrigue and a custom look to sauna walls and ceilings. It’s great look for public saunas, or anyone who wants to something a little different than standard tongue and groove.
Thermo-Aspen is an elegant wall and ceiling cladding for saunas that has been meticulously processed using only heat and steam by Thermory, the global leader in Thermal Modification. The result is a darkened, smooth wood that won’t shrink, warp, cup, or rot when properly installed. Choose this profile for a modern sauna that still feels traditional. Kyte walls can also be harnessed with basic lighting strips behind the benches to creat intrigue and shadow effects.
At Sauna Marketplace, we make it easy with matching benches, backrests, bench skirts, vent hatches, floor grids, and more.
Actual wall coverage is 3.1″.
Thermo-Aspen 5/4×3 STEP Wall Cladding – Sauna Wood by Thermory
$3.72 – $223.97Step up your game and build the sauna of your dreams with STEP Cladding by Thermory. The broad, square grooves create a striking shadow effect adding depth and intrigue to any space. It’s our go-to for vertical wall cladding in any high-end sauna build.
Thermo-Aspen is an elegant wall and ceiling cladding for saunas that has been meticulously processed using only heat and steam by Thermory, the global leader in Thermal Modification. The result is a darkened, smooth wood that won’t shrink, warp, cup, or rot when properly installed. Choose this profile for a classic sauna look that’s more refined than typical North American saunas.
At Sauna Marketplace, we make it easy with matching benches, backrests, bench skirts, vent hatches, floor grids, and more.
Actual wall coverage is 2.2″ which completes the step.
1X5 Thermo-Aspen STS4 Wall Cladding – Thermally Modified Sauna Wood by Thermory
$3.93 – $236.00Wide plank Thermally Modified Aspen (TASP) is an elegant wall and ceiling cladding for saunas that has been meticulously processed using only heat and steam by Thermory, the global leader in Thermal Modification. The result is a darkened, smooth wood that won’t shrink, warp, cup, or rot when properly installed. Choose this profile for a classic sauna look that’s more refined than typical North American saunas.
Working with Tongue and Groove STS4 is a delight for contractors and DIY Sauna Builders alike. We’re not exagerating that every builder we work with has found the quality and consistency to be truly remarkable. At Sauna Marketplace, we make it easy with matching benches, backrests, bench skirts, vent hatches, floor grids, and more.
Actual wall coverage is 4.3″.
Prebuilt Bench Skirt by Thermory
$275.00It’s easier than ever to complete your sauna with a prebuilt sauna bench skirt in thermally modified Aspen or Alder.
Wood Headrest in Thermal Aspen by Thermory
$91.00Match your aesthetic of an all Thermory sauna with a classic thermo-aspen wooden headrest. Aspen is an ideal sauna material because it doesn’t secrete resin, create splinters, or get too hot. The color of thermo-aspen is an attractive golden brown.
Thermory Prebuilt Sauna Backrest
$330.00Ready-to-install sauna backrests from Thermory – the quick and easy solution in good taste. Pairs perfectly with our prebuilt bench modules to make the DIY sauna easier with a more professional result.
Thermo-Aspen Moulding 1×2 Transition T by Thermory
$2.36 – $37.76Need longer boards than available by Thermory? We make those transitions easy with this T moulding to avoid gaps with a professional look. Common on walls and ceilings in commercial saunas.
Note: These will arrive directly from Thermory USA in bundles of two in 7′ and 8′ lengths.
Thermo-Aspen Moulding 1×1 SI Sauna Ceiling Trim By Thermory
$2.00 – $62.40Thermory Thermo-Aspen 1×1 SI makes sauna building easier than ever. These 0.59″x 0.71″ are ideal for concealing the gap and giving a professional finish to any wall to ceiling transition. Make it easy, make it beautiful with Thermory 1×1 ceiling mouldings in Thermo-Aspen.
Note: These will arrive directly from Thermory USA in bundles of four in 7′ and 8′ lengths.
Thermory Medium Squares With Terrace and L-Bench — Models No 42 With Window & No 43
$7,280.00 – $7,835.00Extend your entertainment area with the ultimate relaxation destination. Thermory 40 Series “Medium” squares can bathe two to four people in heat and steam. Customize yours with an extra-wide window. Plus, all Thermory models come with a rain jacket for all-weather protection.
Prebuilt Sauna Bench Modules
$467.00Prebuilt sauna bench modules make it easier than ever to create a high-end DIY sauna in any space. Expandable to any size, and taking corners seamlessly with degree fan-modules that be nearly impossible to build on site.
Thermory Modern Black Sauna Door | Premium Aspen
$1,195.00It’s here! A premium, modern black sauna door from Thermory. With gray glass, sleek black hardware, and painted alder frame. This door contrasts beautifully with any sauna aesthetic. Arrives pre-hung in a reversible frame, making the installation a breeze.
Thermo-Aspen Sauna Floor Grid
Say goodbye to cold feet! This is easiest way to add some comfort and warmth to your sauna floor. This rolling floor grid makes maintenance, cleaning, and drying out of your sauna easier than ever. Thermory’s thermal modification process ensures a long-lasting, beautiful wood finish with minimal maintenance.
Dimensions: .55″ x 31.5″ x 35.4″ (14x800x900)
Sauna Stool or Step in Thermo-Aspen
$419.00This versatile stool can act as a moveable sauna bench, first step, or changing room seat. Dimensions are 15.7″ x 27.6′ (140x400x700).
Thermory Adjustable Air Hatch in Thermally Modified Aspen
$69.00Adjustable Sauna Ventilation Hatch, .5″ x 5.2″ x 11″. In Alder, Aspen, or Thermo-Aspen
Thermory Ignite Black Barrel Sauna
$7,170.00 – $9,000.00Good luck looking away from these showstoppers. Thermory Ignite skillfully emulates the burnt aesthetic of shou sugi ban, yet delivers the resilience and constancy only achievable through natural thermal modification. The resulting blend of old-world tradition and modern appeal could last for decades.
Based on our best-selling Thermory Barrel Saunas.
Thermory Sauna Door | Premium, Thermo Aspen frame
$1,095.00The most trusted sauna door in Europe is now available in North America! Thermory is the global leader in sustainable wood products, and known for sauna material and products. Their glass doors are beautifully framed in by some of their most popular sauna woods: alder, thermo-aspen, and aspen. The choice is yours.
It’s also available in with a wood handle or ‘premium’ hardware kit but we think the basic wood option is just as nice. With either option, the hinges are commercial grade to European standards and adjustable to get a perfect seal. These doors promote an inviting welcome to your sauna.
Contact Sauna Marketplace for additional finishes and custom options, including Thermory’s new black trendline, premium, and classic black sauna doors.
Sauna Squares by Thermory
Where expansive views and rolling steam come easy! The Thermory Square is the ideal sauna for hosting friends, stretching out, or laying down. The L-Bench comfortably seats six, all on the upper benches where optimal heat and steam envelop the bather, guided by the curved contours. It’s remarkably sturdy, and assembly is a breeze. How do we know? Our founder still has the first Square #40 that came over from Europe. Book a free consultation below and we’ll walk you through it.
Thermory Barrel Sauna Kit | 60 Series with Optional Porch and Panoramic Window
Experience the barrel sauna that changed everything. Crafted from the world’s best thermally modified Nordic spruce for unmatched durability and moisture resistance, these saunas feature a curved design for efficient heat circulation, ensuring continuous warmth with less energy. Designed for easy assembly, they come with pre-cut and pre-milled components, allowing quick setup. Available in various configurations, including options with windows and porches, each model provides a spacious and comfortable environment for relaxation and socialization, free from technological distractions.
Thermory Cozy Barrel Sauna | 50 Series
Get America’s most loved barrel sauna by the global leader in sustainable thermal modification. The Thermory 50 series is built to outlast and outperform cedar saunas at an affordable price. The quality is undeniable and requires less maintenance than conventional barrel saunas.
The Thermory 50 Series consists of 3 sizes – each with an optional half-panoramic window in the back. They are the little brother to the more spacious Thermory 60 Series, but still have enough room to stand, stretch, and safely move around.
The flat, 19″ benches are great for laying down or putting your feet up. All Thermory barrel saunas come with a rain jacket and flat floor kit. The 50 Series ships quickly from Thermory USA outside of Buffalo, NY.
For the larger 60 series Thermory Barrel Saunas with porch option, click here.
Thermory Square No 45 | One-Person Outdoor Sauna Kit
$4,980.00The most compact, practical 1-person outdoor sauna kit we’ve ever seen. Thermory Square No 55 redefines what’s possible for a small sauna. This sauna can last a lifetime with thermally modified Nordic Spruce wood that resists warping, cracking, decay that degrades standard outdoor sauna kits.
Thermo-Aspen Moulding 1×1 SHP Sauna Trim, Floor, and Bench Wood By Thermory
$2.00 – $200.00Thermory Thermo-Aspen 1×1 SHP is a versatile sauna material meant for trim, benches, internal corner moulding, and sauna floors. Aspen is a smooth, cool timber to feel against bare skin. Because it doesn’t secrete resin, splinter or overheat, aspen makes for an ideal sauna material. The color of thermally modified aspen is an attractive golden brown. Thermally modified wood resists rotting, expansion, contraction, warping, and cupping.
These 0.83″ thick boards are ideal for creative projects and making your sauna design truly unique.
Note: These can only be purchased in bundles of 10 in 7′ and 8′ lengths.