Convert Macedonian Denar (MKD) to Brazilian Real (BRL)

1 macedonian_denar = 1 macedonian_denar

Exchange rates last updated: February 12, 2026 12:00

Conversion Formula for Macedonian Denar to Brazilian Real

The formula of conversion of Macedonian Denar to Brazilian Real is very simple. To convert Macedonian Denar to Brazilian Real, we can use this simple formula:

1 Macedonian Denar = 9.991201725 Brazilian Real

1 Brazilian Real = 0.1000880602 Macedonian Denar

One Macedonian Denar is equal to 9.991201725 Brazilian Real. So, we need to multiply the number of Macedonian Denar by 9.991201725 to get the no of Brazilian Real. This formula helps when we need to change the measurements from Macedonian Denar to Brazilian Real

Macedonian Denar to Brazilian Real Conversion

The conversion of Macedonian Denar currency to Brazilian Real currency is very simple. Since, as discussed above, One Macedonian Denar is equal to 9.991201725 Brazilian Real. So, to convert Macedonian Denar to Brazilian Real, we must multiply no of Macedonian Denar to 9.991201725. Example:-

Macedonian Denar Brazilian Real
0.01 Macedonian Denar 0.0999120173 Brazilian Real
0.1 Macedonian Denar 0.9991201725 Brazilian Real
1 Macedonian Denar 9.991201725 Brazilian Real
2 Macedonian Denar 19.98240345 Brazilian Real
3 Macedonian Denar 29.973605175 Brazilian Real
5 Macedonian Denar 49.956008625 Brazilian Real
10 Macedonian Denar 99.91201725 Brazilian Real
20 Macedonian Denar 199.8240345 Brazilian Real
50 Macedonian Denar 499.56008625 Brazilian Real
100 Macedonian Denar 999.1201725001 Brazilian Real
500 Macedonian Denar 4,995.6008625005 Brazilian Real
1,000 Macedonian Denar 9,991.201725001 Brazilian Real

Details for Macedonian Denar (MKD) Currency

Introduction : The Macedonian Denar (MKD), symbolized as 'ден', is the official currency of North Macedonia. It plays a vital role in the country's economic framework and daily life, facilitating trade, salaries, taxation, and all financial transactions. Introduced after the country's independence, the Denar represents more than just money—it is a symbol of national sovereignty and economic stability. It is commonly used across urban and rural regions for both retail and commercial activities. The currency’s name, derived from the Roman 'denarius', pays homage to historical roots while supporting a modern and independent monetary system.

History & Origin : The Macedonian Denar was introduced in 1992 following the breakup of Yugoslavia, replacing the Yugoslav Dinar. Initially, it was released as a transitional currency before being restructured into the 'new Denar' in 1993 at a rate of 100:1. This move stabilized the fledgling economy and allowed North Macedonia to assert its financial independence. The currency has since evolved with modern banknotes and coins that feature significant historical figures and cultural motifs of the country. The National Bank of the Republic of North Macedonia manages monetary policy and ensures the stability of the Denar in both domestic and regional markets.

Current Use : The Macedonian Denar is used for all forms of payment within North Macedonia, including retail shopping, service industries, transportation, and government-related financial activities. The Denar is subdivided into 100 deni, though coins of such small denomination are rarely used in modern transactions. While not widely traded on international forex markets, the Denar is stable within the region. North Macedonia is a candidate for EU membership, and if accepted, it may eventually adopt the Euro. However, for now, the Denar continues to be a reliable and locally trusted medium of exchange, essential to everyday life in the country.

Details of North Macedonia

North Macedonia is a landlocked country located in the heart of the Balkan Peninsula in Southeastern Europe. With a diverse cultural heritage and a population of around two million, it is known for its scenic landscapes, historic architecture, and a mixture of Mediterranean and Slavic influences. The capital city, Skopje, serves as the political, economic, and cultural center of the country, showcasing a blend of Ottoman, Byzantine, and modern architectural styles.

The country declared independence from the former Yugoslavia in 1991 and has undergone significant political and economic reforms since then. North Macedonia has made efforts to integrate into Euro-Atlantic institutions and became a NATO member in 2020. It is also in negotiations for European Union membership, which continues to shape its domestic policies and regional relations.

North Macedonia's economy is moderately diversified, with key sectors including agriculture, manufacturing, energy, and services. It is well known for its production of wine, textiles, and various agricultural goods. Tourism has grown steadily, with travelers drawn to natural attractions like Lake Ohrid, a UNESCO World Heritage Site, and the country's rugged mountains and historic monasteries.

The population is ethnically diverse, with Macedonians making up the majority, alongside significant Albanian, Turkish, Roma, and Serbian communities. This cultural variety is reflected in the country's languages, cuisine, and traditions. Macedonian is the official language, and Albanian holds co-official status in some regions.

Education and healthcare systems have improved in recent years, with continued support from international partners. While challenges remain, especially related to employment and youth migration, North Macedonia is steadily moving toward greater regional integration and economic development. It continues to balance tradition with progress in its journey as a modern European nation.

Details for Brazilian Real (BRL) Currency

Introduction : The Brazilian Real (R$), abbreviated as BRL in global financial systems, is the official currency of Brazil. Introduced as part of a major economic reform, the Real is issued and regulated by the Central Bank of Brazil. Subdivided into 100 centavos, the currency is used in everyday transactions, from local markets to international business. The Real is known for its vibrant banknotes featuring iconic Brazilian fauna and historical figures. It serves as a key symbol of national economic identity and plays a vital role in Brazil’s domestic stability and international trade operations across Latin America and beyond.

History & Origin : The Brazilian Real was introduced on July 1, 1994, as part of the Plano Real, a successful economic stabilization plan launched to combat hyperinflation that plagued Brazil during the late 20th century. The Real replaced the cruzeiro real at a rate of 1 Real = 2,750 cruzeiros reais. Initially pegged to the US Dollar to curb inflation and stabilize purchasing power, the currency moved to a floating exchange rate system in 1999. Over the years, the Real has undergone several changes in design and security features, reflecting Brazil's evolving economy and commitment to anti-counterfeiting measures.

Current Use : The Brazilian Real is used across all economic levels in Brazil—from informal vendors and public transit to online banking and international finance. It is accepted throughout the country for every kind of transaction, and digital payment systems and mobile banking have increased its accessibility in recent years. The currency is also used in trade with neighboring countries and by tourists visiting Brazil. While its value has fluctuated in response to global market shifts, the Real remains a vital part of Brazil’s economic infrastructure and a reflection of its financial resilience and national identity.

Details of Brazil

Brazil, officially the Federative Republic of Brazil, is the largest country in South America and the fifth-largest in the world by both area and population. It spans a vast territory that includes the Amazon rainforest, the world’s largest tropical forest, as well as diverse ecosystems, mountains, beaches, and savannas. The country shares borders with every South American nation except Chile and Ecuador.

Brazil’s capital is Brasília, a modernist city designed by architect Oscar Niemeyer, while São Paulo and Rio de Janeiro serve as its largest and most influential urban centers. The country’s official language is Portuguese, making it unique in a region where Spanish predominates. Brazil is known for its vibrant culture, expressed through its music, dance, cuisine, and festivals, especially the world-famous Carnival celebration held each year before Lent.

The Brazilian economy is one of the largest in the world and is based on agriculture, mining, manufacturing, and services. Brazil is a leading exporter of commodities such as soybeans, iron ore, coffee, and oil. It is also home to large domestic industries in automobiles, aircraft, and renewable energy. Despite its economic potential, Brazil faces challenges like inequality, political instability, and infrastructure deficits.

Brazil is a multicultural society with a population that includes people of Indigenous, European, African, and Asian descent. This diversity is reflected in its social customs, religious practices, and daily life. As a member of BRICS and a major player in regional politics, Brazil exerts considerable influence on global and Latin American affairs. Its natural beauty, cultural richness, and dynamic society make it one of the most captivating and complex nations on Earth.

Convert Macedonian Denar to Other Currencies

Macedonian Denar to United Arab Emirates DirhamUnited Arab Emirates Dirham to Macedonian Denar
Macedonian Denar to Afghan AfghaniAfghan Afghani to Macedonian Denar
Macedonian Denar to Albanian LekAlbanian Lek to Macedonian Denar
Macedonian Denar to Armenian DramArmenian Dram to Macedonian Denar
Macedonian Denar to Netherlands Antillean GuilderNetherlands Antillean Guilder to Macedonian Denar
Macedonian Denar to Angolan KwanzaAngolan Kwanza to Macedonian Denar
Macedonian Denar to Argentine PesoArgentine Peso to Macedonian Denar
Macedonian Denar to Australian DollarAustralian Dollar to Macedonian Denar
Macedonian Denar to Aruban FlorinAruban Florin to Macedonian Denar
Macedonian Denar to Azerbaijani ManatAzerbaijani Manat to Macedonian Denar
Macedonian Denar to Bosnia Herzegovina Convertible MarkBosnia Herzegovina Convertible Mark to Macedonian Denar
Macedonian Denar to Barbadian DollarBarbadian Dollar to Macedonian Denar
Macedonian Denar to Bangladeshi TakaBangladeshi Taka to Macedonian Denar
Macedonian Denar to Bulgarian LevBulgarian Lev to Macedonian Denar
Macedonian Denar to Bahraini DinarBahraini Dinar to Macedonian Denar
Macedonian Denar to Burundian FrancBurundian Franc to Macedonian Denar
Macedonian Denar to Bermudan DollarBermudan Dollar to Macedonian Denar
Macedonian Denar to Brunei DollarBrunei Dollar to Macedonian Denar
Macedonian Denar to Bolivian BolivianoBolivian Boliviano to Macedonian Denar
Macedonian Denar to Brazilian RealBrazilian Real to Macedonian Denar
Macedonian Denar to Bahamian DollarBahamian Dollar to Macedonian Denar
Macedonian Denar to Bhutanese NgultrumBhutanese Ngultrum to Macedonian Denar
Macedonian Denar to Botswanan PulaBotswanan Pula to Macedonian Denar
Macedonian Denar to Belarusian RubleBelarusian Ruble to Macedonian Denar
Macedonian Denar to Belize DollarBelize Dollar to Macedonian Denar
Macedonian Denar to Canadian DollarCanadian Dollar to Macedonian Denar
Macedonian Denar to Congolese FrancCongolese Franc to Macedonian Denar
Macedonian Denar to Swiss FrancSwiss Franc to Macedonian Denar
Macedonian Denar to Chilean Unit Of Account UfChilean Unit Of Account Uf to Macedonian Denar
Macedonian Denar to Chilean PesoChilean Peso to Macedonian Denar
Macedonian Denar to Chinese Yuan OffshoreChinese Yuan Offshore to Macedonian Denar
Macedonian Denar to Chinese YuanChinese Yuan to Macedonian Denar
Macedonian Denar to Colombian PesoColombian Peso to Macedonian Denar
Macedonian Denar to Costa Rican ColonCosta Rican Colon to Macedonian Denar
Macedonian Denar to Cuban Convertible PesoCuban Convertible Peso to Macedonian Denar
Macedonian Denar to Cuban PesoCuban Peso to Macedonian Denar
Macedonian Denar to Cape Verdean EscudoCape Verdean Escudo to Macedonian Denar
Macedonian Denar to Czech Republic KorunaCzech Republic Koruna to Macedonian Denar
Macedonian Denar to Djiboutian FrancDjiboutian Franc to Macedonian Denar
Macedonian Denar to Danish KroneDanish Krone to Macedonian Denar
Macedonian Denar to Dominican PesoDominican Peso to Macedonian Denar
Macedonian Denar to Algerian DinarAlgerian Dinar to Macedonian Denar
Macedonian Denar to Egyptian PoundEgyptian Pound to Macedonian Denar
Macedonian Denar to Eritrean NakfaEritrean Nakfa to Macedonian Denar
Macedonian Denar to Ethiopian BirrEthiopian Birr to Macedonian Denar
Macedonian Denar to EuroEuro to Macedonian Denar
Macedonian Denar to Fijian DollarFijian Dollar to Macedonian Denar
Macedonian Denar to Falkland Islands PoundFalkland Islands Pound to Macedonian Denar
Macedonian Denar to British Pound SterlingBritish Pound Sterling to Macedonian Denar
Macedonian Denar to Georgian LariGeorgian Lari to Macedonian Denar
Macedonian Denar to Guernsey PoundGuernsey Pound to Macedonian Denar
Macedonian Denar to Ghanaian CediGhanaian Cedi to Macedonian Denar
Macedonian Denar to Gibraltar PoundGibraltar Pound to Macedonian Denar
Macedonian Denar to Gambian DalasiGambian Dalasi to Macedonian Denar
Macedonian Denar to Guinean FrancGuinean Franc to Macedonian Denar
Macedonian Denar to Guatemalan QuetzalGuatemalan Quetzal to Macedonian Denar
Macedonian Denar to Guyanaese DollarGuyanaese Dollar to Macedonian Denar
Macedonian Denar to Hong Kong DollarHong Kong Dollar to Macedonian Denar
Macedonian Denar to Honduran LempiraHonduran Lempira to Macedonian Denar
Macedonian Denar to Haitian GourdeHaitian Gourde to Macedonian Denar
Macedonian Denar to Hungarian ForintHungarian Forint to Macedonian Denar
Macedonian Denar to Indonesian RupiahIndonesian Rupiah to Macedonian Denar
Macedonian Denar to Israeli New SheqelIsraeli New Sheqel to Macedonian Denar
Macedonian Denar to Manx PoundManx Pound to Macedonian Denar
Macedonian Denar to Indian RupeeIndian Rupee to Macedonian Denar
Macedonian Denar to Iraqi DinarIraqi Dinar to Macedonian Denar
Macedonian Denar to Iranian RialIranian Rial to Macedonian Denar
Macedonian Denar to Icelandic KronaIcelandic Krona to Macedonian Denar
Macedonian Denar to Jersey PoundJersey Pound to Macedonian Denar
Macedonian Denar to Jamaican DollarJamaican Dollar to Macedonian Denar
Macedonian Denar to Jordanian DinarJordanian Dinar to Macedonian Denar
Macedonian Denar to Japanese YenJapanese Yen to Macedonian Denar
Macedonian Denar to Kenyan ShillingKenyan Shilling to Macedonian Denar
Macedonian Denar to Kyrgystani SomKyrgystani Som to Macedonian Denar
Macedonian Denar to Cambodian RielCambodian Riel to Macedonian Denar
Macedonian Denar to Comorian FrancComorian Franc to Macedonian Denar
Macedonian Denar to North Korean WonNorth Korean Won to Macedonian Denar
Macedonian Denar to South Korean WonSouth Korean Won to Macedonian Denar
Macedonian Denar to Kuwaiti DinarKuwaiti Dinar to Macedonian Denar
Macedonian Denar to Cayman Islands DollarCayman Islands Dollar to Macedonian Denar
Macedonian Denar to Kazakhstani TengeKazakhstani Tenge to Macedonian Denar
Macedonian Denar to Laotian KipLaotian Kip to Macedonian Denar
Macedonian Denar to Lebanese PoundLebanese Pound to Macedonian Denar
Macedonian Denar to Sri Lankan RupeeSri Lankan Rupee to Macedonian Denar
Macedonian Denar to Liberian DollarLiberian Dollar to Macedonian Denar
Macedonian Denar to Lesotho LotiLesotho Loti to Macedonian Denar
Macedonian Denar to Libyan DinarLibyan Dinar to Macedonian Denar
Macedonian Denar to Moroccan DirhamMoroccan Dirham to Macedonian Denar
Macedonian Denar to Moldovan LeuMoldovan Leu to Macedonian Denar
Macedonian Denar to Malagasy AriaryMalagasy Ariary to Macedonian Denar
Macedonian Denar to Myanma KyatMyanma Kyat to Macedonian Denar
Macedonian Denar to Mongolian TugrikMongolian Tugrik to Macedonian Denar
Macedonian Denar to Macanese PatacaMacanese Pataca to Macedonian Denar
Macedonian Denar to Mauritanian OuguiyaMauritanian Ouguiya to Macedonian Denar
Macedonian Denar to Mauritian RupeeMauritian Rupee to Macedonian Denar
Macedonian Denar to Maldivian RufiyaaMaldivian Rufiyaa to Macedonian Denar
Macedonian Denar to Malawian KwachaMalawian Kwacha to Macedonian Denar
Macedonian Denar to Mexican PesoMexican Peso to Macedonian Denar
Macedonian Denar to Malaysian RinggitMalaysian Ringgit to Macedonian Denar
Macedonian Denar to Mozambican MeticalMozambican Metical to Macedonian Denar
Macedonian Denar to Namibian DollarNamibian Dollar to Macedonian Denar
Macedonian Denar to Nigerian NairaNigerian Naira to Macedonian Denar
Macedonian Denar to Nicaraguan CordobaNicaraguan Cordoba to Macedonian Denar
Macedonian Denar to Norwegian KroneNorwegian Krone to Macedonian Denar
Macedonian Denar to Nepalese RupeeNepalese Rupee to Macedonian Denar
Macedonian Denar to New Zealand DollarNew Zealand Dollar to Macedonian Denar
Macedonian Denar to Omani RialOmani Rial to Macedonian Denar
Macedonian Denar to Panamanian BalboaPanamanian Balboa to Macedonian Denar
Macedonian Denar to Peruvian Nuevo SolPeruvian Nuevo Sol to Macedonian Denar
Macedonian Denar to Papua New Guinean KinaPapua New Guinean Kina to Macedonian Denar
Macedonian Denar to Philippine PesoPhilippine Peso to Macedonian Denar
Macedonian Denar to Pakistani RupeePakistani Rupee to Macedonian Denar
Macedonian Denar to Polish ZlotyPolish Zloty to Macedonian Denar
Macedonian Denar to Paraguayan GuaraniParaguayan Guarani to Macedonian Denar
Macedonian Denar to Qatari RialQatari Rial to Macedonian Denar
Macedonian Denar to Romanian LeuRomanian Leu to Macedonian Denar
Macedonian Denar to Serbian DinarSerbian Dinar to Macedonian Denar
Macedonian Denar to Russian RubleRussian Ruble to Macedonian Denar
Macedonian Denar to Rwandan FrancRwandan Franc to Macedonian Denar
Macedonian Denar to Saudi RiyalSaudi Riyal to Macedonian Denar
Macedonian Denar to Solomon Islands DollarSolomon Islands Dollar to Macedonian Denar
Macedonian Denar to Seychellois RupeeSeychellois Rupee to Macedonian Denar
Macedonian Denar to Sudanese PoundSudanese Pound to Macedonian Denar
Macedonian Denar to Swedish KronaSwedish Krona to Macedonian Denar
Macedonian Denar to Singapore DollarSingapore Dollar to Macedonian Denar
Macedonian Denar to Saint Helena PoundSaint Helena Pound to Macedonian Denar
Macedonian Denar to Sierra Leonean LeoneSierra Leonean Leone to Macedonian Denar
Macedonian Denar to Somali ShillingSomali Shilling to Macedonian Denar
Macedonian Denar to Surinamese DollarSurinamese Dollar to Macedonian Denar
Macedonian Denar to South Sudanese PoundSouth Sudanese Pound to Macedonian Denar
Macedonian Denar to Sao Tome And Principe DobraSao Tome And Principe Dobra to Macedonian Denar
Macedonian Denar to Salvadoran ColonSalvadoran Colon to Macedonian Denar
Macedonian Denar to Syrian PoundSyrian Pound to Macedonian Denar
Macedonian Denar to Swazi LilangeniSwazi Lilangeni to Macedonian Denar
Macedonian Denar to Thai BahtThai Baht to Macedonian Denar
Macedonian Denar to Tajikistani SomoniTajikistani Somoni to Macedonian Denar
Macedonian Denar to Turkmenistani ManatTurkmenistani Manat to Macedonian Denar
Macedonian Denar to Tunisian DinarTunisian Dinar to Macedonian Denar
Macedonian Denar to Tongan PaangaTongan Paanga to Macedonian Denar
Macedonian Denar to Turkish LiraTurkish Lira to Macedonian Denar
Macedonian Denar to Trinidad And Tobago DollarTrinidad And Tobago Dollar to Macedonian Denar
Macedonian Denar to New Taiwan DollarNew Taiwan Dollar to Macedonian Denar
Macedonian Denar to Tanzanian ShillingTanzanian Shilling to Macedonian Denar
Macedonian Denar to Ukrainian HryvniaUkrainian Hryvnia to Macedonian Denar
Macedonian Denar to Ugandan ShillingUgandan Shilling to Macedonian Denar
Macedonian Denar to United States DollarUnited States Dollar to Macedonian Denar
Macedonian Denar to Uruguayan PesoUruguayan Peso to Macedonian Denar
Macedonian Denar to Uzbekistan SomUzbekistan Som to Macedonian Denar
Macedonian Denar to Venezuelan Bolivar SoberanoVenezuelan Bolivar Soberano to Macedonian Denar
Macedonian Denar to Vietnamese DongVietnamese Dong to Macedonian Denar
Macedonian Denar to Vanuatu VatuVanuatu Vatu to Macedonian Denar
Macedonian Denar to Samoan TalaSamoan Tala to Macedonian Denar
Macedonian Denar to Cfa Franc BeacCfa Franc Beac to Macedonian Denar
Macedonian Denar to Silver Troy OunceSilver Troy Ounce to Macedonian Denar
Macedonian Denar to Gold Troy OunceGold Troy Ounce to Macedonian Denar
Macedonian Denar to East Caribbean DollarEast Caribbean Dollar to Macedonian Denar
Macedonian Denar to Special Drawing RightsSpecial Drawing Rights to Macedonian Denar
Macedonian Denar to Cfa Franc BceaoCfa Franc Bceao to Macedonian Denar
Macedonian Denar to Palladium OuncePalladium Ounce to Macedonian Denar
Macedonian Denar to Cfp FrancCfp Franc to Macedonian Denar
Macedonian Denar to Platinum OuncePlatinum Ounce to Macedonian Denar
Macedonian Denar to Yemeni RialYemeni Rial to Macedonian Denar
Macedonian Denar to South African RandSouth African Rand to Macedonian Denar
Macedonian Denar to Zambian KwachaZambian Kwacha to Macedonian Denar

FAQ on Macedonian Denar (MKD) to Brazilian Real (BRL) Conversion:

What is the Symbol of Macedonian Denar and Brazilian Real?

The symbol for Macedonian Denar is 'ден', and for Brazilian Reals, it is 'R$'. These symbols are used to denote in everyday currency analysis.

How to convert Macedonian Denar(s) to Brazilian Real(es)?

To convert Macedonian Denar(s) to Brazilian Real(es), multiply the number of Macedonian Denars by 9.991201725001 because one Macedonian Denar equals 9.991201725001 Brazilian Reals.
Formula: Brazilian Reals = Macedonian Denars × 9.991201725001.
This is a standard rule used in conversions.

How to convert Brazilian Real(es) to Macedonian Denar(s) ?

To convert Brazilian Real(es) to Macedonian Denar(s), divide the number of Brazilian Reals by 9.991201725001, since, 1 Macedonian Denar contains exactly 9.991201725001 Brazilian Real(es).
Formula: Macedonian Denars = Brazilian Real(s) ÷ 9.991201725001.
It’s a common calculation in conversions.

How many Macedonian Denar(s) are these in an Brazilian Real(es) ?

There are 0.1000880602278 Macedonian Denars in one Brazilian Real. This is derived by dividing 1 Brazilian Real by 9.991201725001, as 1 Macedonian Denar equals 9.991201725001 Brazilian Real(s).
Formula: Macedonian Denar = Brazilian Reals ÷ 9.991201725001.
It’s a precise currency conversion method.

How many Brazilian Real(es) are these in an Macedonian Denar(s) ?

There are exactly 9.991201725001 Brazilian Reals in one Macedonian Denar. This is a fixed value used in the measurement system.
Formula: Brazilian Real(s) = Macedonian Denars × 9.991201725001.
It's one of the most basic conversions.

How many Brazilian Real in 10 Macedonian Denar?

There are 99.91201725001 Brazilian Reals in 10 Macedonian Denars. This is calculated by multiplying 10 by 9.991201725001.
Formula: 10 Macedonian Denars × 9.991201725001 = 99.91201725001 Brazilian Reals.
This conversion is helpful for measurements.

How many Brazilian Real(s) in 50 Macedonian Denar?

There are 499.56008625005 Brazilian Reals in 50 Macedonian Denars. One can calculate it by multiplying 50 by 9.991201725001.
Formula: 50 Macedonian Denars × 9.991201725001 = 499.56008625005 Brazilian Reals.
This conversion is used in many applications.

How many Brazilian Real(s) in 100 Macedonian Denar?

There are 999.1201725001 Brazilian Real(s) in 100 Macedonian Denars. Multiply 100 by 9.991201725001 to get the result.
Formula: 100 Macedonian Denars × 9.991201725001 = 999.1201725001 Brazilian Real(s).
This is a basic currency conversion formula.