Cryptocurrency Conversion Guide: Bitcoin, Ethereum, and Beyond Cryptocurrency conversion is a fundamental skill for anyone working with digital assets—whether you are an investor, developer, engineer, scientist, or everyday user. This guide explains the key concepts, unit systems, precise conversion formulas, worked numerical examples, and practical tips to convert between cryptocurrencies (Bitcoin, Ethereum), fiat currencies, and token denominations safely and accurately. Introduction Cryptocurrencies use native units and smallest divisible subunits that differ from fiat currencies. Conversions are needed for trading, accounting, fee estimation, resource billing, research, and embedded systems that interact with blockchains. Common conversion tasks include: Converting BTC ↔ USD or ETH ↔ EUR Converting BTC ↔ ETH via market rates Translating on-chain raw values (satoshis, wei) to human-readable amounts Calculating gas fees (gwei × gas used → ETH → USD) Handling token decimals (ERC-20 tokens using 6–18 decimals) Accurate conversions require attention to exchange rates, unit scales, fees, and numerical precision. Key Concepts/Definitions Bitcoin (BTC): A cryptocurrency where the smallest unit is a satoshi. 1 BTC = 100,000,000 satoshis (1e8 satoshis). Ethereum (ETH): A cryptocurrency where the smallest unit is wei. 1 ETH = 1,000,000,000,000,000,000 wei (1e18 wei). gwei is commonly used for gas price (1 gwei = 1e9 wei). Exchange rate: The market price between two currencies or assets, e.g., BTC/USD or ETH/BTC. On-chain raw amount: Integer value stored on-chain (e.g., token amount in smallest units). To get human-readable amount: token_amount = raw_amount / (10^decimals) Slippage: Difference between expected and executed price due to market movement during a trade. Gas: Fee unit for Ethereum transactions; calculated as gas_used × gas_price (in wei). Stablecoin: A token pegged to a fiat currency (e.g., USDC ~ USD) often with different decimals (USDC typically 6 decimals). Precision and rounding: Use integer or fixed-point arithmetic when possible to avoid floating-point rounding errors in financial contexts. Conversion Formulas Here are the core formulas you will use repeatedly. Bolded for clarity. Convert cryptocurrency amount to fiat: fiat_value = crypto_amount × crypto_price_in_fiat Example: USD = BTC × (USD per BTC) Convert fiat to cryptocurrency: crypto_amount = fiat_value / crypto_price_in_fiat Convert between two cryptocurrencies (A → B) using prices in a common fiat: A_to_B = (A_amount × price_A_in_fiat) / price_B_in_fiat Alternatively, use direct pair price price_A_in_B, then B_amount = A_amount × price_A_in_B Convert on-chain raw integer to human-readable token amount: readable_amount = raw_amount / (10^decimals) Convert human-readable token amount to raw integer: raw_amount = readable_amount × (10^decimals) Convert wei/gwei to ETH: ETH = wei / 1e18 ETH = gwei × 1e9 / 1e18 = gwei / 1e9 Gas fee (ETH) calculation: gas_fee_ETH = gas_used × gas_price_in_wei / 1e18 Fee in fiat: fee_fiat = gas_fee_ETH × ETH_price_in_fiat Always include adequate decimal places during intermediate calculations; round only for display. Practical Examples (with worked calculations) Below are step-by-step, numerical examples for common conversion tasks. Example 1 — Convert BTC to USD Given: 0.125 BTC, BTC price = $40,000 / BTC Formula: USD = BTC × (USD per BTC) Calculation: 1. USD = 0.125 × 40,000 2. USD = 5,000 Result: 0.125 BTC = $5,000 Example 2 — Convert Satoshis to BTC Given: 15,000,000 satoshis Formula: BTC = satoshis / 1e8 Calculation: 1. BTC = 15,000,000 / 100,000,000 2. BTC = 0.15 Result: 15,000,000 satoshis = 0.15 BTC Example 3 — Convert ETH to BTC using fiat intermediary Given: 2.5 ETH, ETH price = $2,500, BTC price = $40,000 Formula: BTC = (ETH_amount × ETH_price) / BTC_price Calculation: 1. ETH value in USD = 2.5 × 2,500 = 6,250 USD 2. BTC amount = 6,250 / 40,000 = 0.15625 BTC Result: 2.5 ETH ≈ 0.15625 BTC Example 4 — Convert ETH to BTC using direct pair price Given direct market: 1 ETH = 0.063 BTC, convert 3 ETH Formula: BTC = ETH_amount × price_ETH_in_BTC Calculation: 1. BTC = 3 × 0.063 = 0.189 BTC Result: 3 ETH = 0.189 BTC Example 5 — Wei/Gwei and gas fee calculation (ETH) Given: gas used = 21,000 (standard ETH transfer), gas price = 50 gwei, ETH price = $2,500 Convert gwei to wei: 50 gwei = 50 × 1e9 = 50,000,000,000 wei Gas fee in ETH: gas_fee_ETH = gas_used × gas_price_wei / 1e18 Calculation: 1. gas_fee_wei = 21,000 × 50,000,000,000 = 1,050,000,000,000,000 (1.05e15) wei 2. gas_fee_ETH = 1.05e15 / 1e18 = 0.00105 ETH Gas fee in USD: fee_USD = gas_fee_ETH × ETH_price Calculation: 1. fee_USD = 0.00105 × 2,500 = $2.625 Result: Gas fee = 0.00105 ETH ≈ $2.63 Example 6 — Token decimals (ERC-20) Given: raw token amount = 3,500,000 units, token decimals = 6 Formula: readable = raw / 10^decimals Calculation: 1. readable = 3,500,000 / 1,000,000 = 3.5 tokens Reverse (settle a payment of 7.25 t