> ## Documentation Index > Fetch the complete documentation index at: https://docs.iotools.cloud/llms.txt > Use this file to discover all available pages before exploring further. # Power Factor Correction Calculator > Calculate the capacitor kvar needed to correct a power factor to a target value, and size the bank itself — capacitance in µF per phase for a delta or star connection, capacitor current, and the apparent power and line current before and after correction. [Try Power Factor Correction Calculator in your browser →](https://iotools.cloud/tool/power-factor-correction-calculator/) ## OpenAPI ````yaml https://api.iotools.cloud/v1/openapi post /v1/tool/power-factor-correction-calculator openapi: 3.1.0 info: title: iotools.cloud API version: 1.0.0 description: >- Run any iotools.cloud tool over HTTP. Authenticate with `Authorization: Bearer iot_live_…`. **Only `POST /v1/tool/{slug}` costs credits.** Every GET here — the catalog, a tool's schema, your balance — is free. A tool call is charged its own weight or your plan's per-call minimum, whichever is larger; `x-iotools-credit-cost` on each operation is quoted at the free-tier minimum, and `GET /v1/tools/list` returns the exact figure for your key. `GET /v1/me/credits` reports what you have left, and `GET /v1/me/usage` reports what it went on. Failures are RFC 9457 problem documents — branch on `code`. servers: - url: https://api.iotools.cloud description: Production security: - bearerAuth: [] tags: - name: Catalog description: Find a tool and read its contract. Free. - name: Converters description: >- Convert between formats, encodings, and units — Base64, CSV and JSON, timestamps, and more. Fast, free, and processed right in your browser. - name: Formatters description: >- Format, beautify, minify, and validate code and data — JSON, HTML, CSS, SQL, and regex. Clean up messy input in one click, with nothing to upload. - name: Generators description: >- Generate exactly what you need and on demand — passwords, UUIDs, QR codes, hashes, random numbers, and more. Secure, instant, and free. - name: Calculators description: >- Crunch the numbers fast — from everyday math to specialized conversions and unit work. Free online calculators that run entirely in your browser. - name: Editors description: >- Edit and transform text, code, and images with quick, focused editors that run entirely in your browser — nothing to install, and no sign-up needed. - name: Utilities description: >- Everyday developer and web utilities — DNS and IP lookups, redirect and certificate checkers, and other quick diagnostics. Free and privacy-friendly. - name: Account description: Your key's allowance, limits and usage history. paths: /v1/tool/power-factor-correction-calculator: post: tags: - Calculators summary: Power Factor Correction Calculator description: >- Calculate the capacitor kvar needed to correct a power factor to a target value, and size the bank itself — capacitance in µF per phase for a delta or star connection, capacitor current, and the apparent power and line current before and after correction. [Try Power Factor Correction Calculator in your browser →](https://iotools.cloud/tool/power-factor-correction-calculator/) operationId: run_power_factor_correction_calculator requestBody: required: false content: application/json: schema: type: object properties: realPower: type: number description: Real Power (kW) minimum: 0 existingPf: type: number description: Existing Power Factor minimum: 0.05 maximum: 1 targetPf: type: number description: Target Power Factor minimum: 0.05 maximum: 1 system: enum: - three - single description: Supply voltage: type: number description: Voltage (V) minimum: 1 frequency: enum: - '50' - '60' description: Frequency connection: enum: - delta - star description: Bank Connection required: [] examples: 100_kw_from_0_75_to_0_95_pf_400_v_three_phase_delta: summary: 100 kW from 0.75 to 0.95 PF, 400 V three-phase delta value: realPower: '100' existingPf: '0.75' targetPf: '0.95' system: three voltage: '400' frequency: '50' connection: delta star_connected_bank_at_60_hz: summary: Star-connected bank at 60 Hz value: realPower: '250' existingPf: '0.8' targetPf: '0.98' system: three voltage: '480' frequency: '60' connection: star single_phase_5_kw_workshop_load_at_230_v: summary: Single-phase 5 kW workshop load at 230 V value: realPower: '5' existingPf: '0.7' targetPf: '0.95' system: single voltage: '230' frequency: '50' connection: delta responses: '200': description: Tool output content: application/json: examples: 100_kw_from_0_75_to_0_95_pf_400_v_three_phase_delta: summary: 100 kW from 0.75 to 0.95 PF, 400 V three-phase delta value: tool: power-factor-correction-calculator tool_version: 1.0.1 outputs: results: - quantity: Power factor before: '0.75' after: '0.95' - quantity: Phase angle φ before: 41.4096° after: 18.1949° - quantity: Real power before: 100 kW after: 100 kW - quantity: Reactive power before: 88.1917 kvar after: 32.8684 kvar - quantity: Apparent power before: 133.333 kVA after: 105.263 kVA - quantity: Line current before: 192.45 A after: 151.934 A capacitor: - item: Required compensation value: 55.3233 kvar - item: kvar per kW (tan φ₁ − tan φ₂) value: '0.553233' - item: Bank connection value: Delta (3 capacitors) - item: Capacitor voltage value: 400 V - item: Capacitance per phase value: 366.874 µF - item: Total capacitance value: 1100.62 µF - item: Capacitor current per phase value: 46.1027 A - item: Capacitor line current value: 79.8523 A - item: Apparent power released value: 28.0702 kVA - item: Line current reduction value: 21.0526 % breakdown: >- φ₁ = acos(0.75) = 41.4096° tan φ₁ = 0.881917 φ₂ = acos(0.95) = 18.1949° tan φ₂ = 0.328684 Qc = P × (tan φ₁ − tan φ₂) = 100 × 0.553233 = 55.3233 kvar S falls from 133.333 kVA to 105.263 kVA, freeing 28.0702 kVA I = S ÷ (√3 × 400 V): 192.45 A → 151.934 A C = (Qc ÷ 3) ÷ (2πf × 400²) = 366.874 µF per phase at 50 Hz Preliminary sizing only — harmonics, detuned reactors, switching steps and utility rules need an engineering review. credits_used: 3 credits_remaining: null star_connected_bank_at_60_hz: summary: Star-connected bank at 60 Hz value: tool: power-factor-correction-calculator tool_version: 1.0.1 outputs: results: - quantity: Power factor before: '0.8' after: '0.98' - quantity: Phase angle φ before: 36.8699° after: 11.4783° - quantity: Real power before: 250 kW after: 250 kW - quantity: Reactive power before: 187.5 kvar after: 50.7647 kvar - quantity: Apparent power before: 312.5 kVA after: 255.102 kVA - quantity: Line current before: 375.879 A after: 306.84 A capacitor: - item: Required compensation value: 136.735 kvar - item: kvar per kW (tan φ₁ − tan φ₂) value: '0.546941' - item: Bank connection value: Star / wye (3 capacitors) - item: Capacitor voltage value: 277.128 V - item: Capacitance per phase value: 1574.23 µF - item: Total capacitance value: 4722.68 µF - item: Capacitor current per phase value: 164.467 A - item: Capacitor line current value: 164.467 A - item: Apparent power released value: 57.398 kVA - item: Line current reduction value: 18.3673 % breakdown: >- φ₁ = acos(0.8) = 36.8699° tan φ₁ = 0.75 φ₂ = acos(0.98) = 11.4783° tan φ₂ = 0.203059 Qc = P × (tan φ₁ − tan φ₂) = 250 × 0.546941 = 136.735 kvar S falls from 312.5 kVA to 255.102 kVA, freeing 57.398 kVA I = S ÷ (√3 × 480 V): 375.879 A → 306.84 A C = (Qc ÷ 3) ÷ (2πf × 277.128²) = 1574.23 µF per phase at 60 Hz Preliminary sizing only — harmonics, detuned reactors, switching steps and utility rules need an engineering review. credits_used: 3 credits_remaining: null single_phase_5_kw_workshop_load_at_230_v: summary: Single-phase 5 kW workshop load at 230 V value: tool: power-factor-correction-calculator tool_version: 1.0.1 outputs: results: - quantity: Power factor before: '0.7' after: '0.95' - quantity: Phase angle φ before: 45.573° after: 18.1949° - quantity: Real power before: 5 kW after: 5 kW - quantity: Reactive power before: 5.10102 kvar after: 1.64342 kvar - quantity: Apparent power before: 7.14286 kVA after: 5.26316 kVA - quantity: Line current before: 31.0559 A after: 22.8833 A capacitor: - item: Required compensation value: 3.4576 kvar - item: kvar per kW (tan φ₁ − tan φ₂) value: '0.69152' - item: Bank connection value: Single-phase - item: Capacitor voltage value: 230 V - item: Capacitance per phase value: 208.051 µF - item: Total capacitance value: 208.051 µF - item: Capacitor current per phase value: 15.033 A - item: Capacitor line current value: 15.033 A - item: Apparent power released value: 1.8797 kVA - item: Line current reduction value: 26.3158 % breakdown: >- φ₁ = acos(0.7) = 45.573° tan φ₁ = 1.0202 φ₂ = acos(0.95) = 18.1949° tan φ₂ = 0.328684 Qc = P × (tan φ₁ − tan φ₂) = 5 × 0.69152 = 3.4576 kvar S falls from 7.14286 kVA to 5.26316 kVA, freeing 1.8797 kVA I = S ÷ 230 V: 31.0559 A → 22.8833 A C = Qc ÷ (2πf V²) = 208.051 µF at 50 Hz Preliminary sizing only — harmonics, detuned reactors, switching steps and utility rules need an engineering review. credits_used: 3 credits_remaining: null schema: type: object required: - tool - tool_version - outputs - credits_used - credits_remaining properties: outputs: type: object properties: results: type: array description: Before & After Correction items: type: object properties: quantity: type: string description: Quantity before: type: string description: Before after: type: string description: After x-iotools-columns: - quantity - before - after capacitor: type: array description: Capacitor Bank items: type: object properties: item: type: string description: Item value: type: string description: Value x-iotools-columns: - item - value breakdown: type: string description: Formula & Breakdown tool: type: string description: The tool's slug, echoing the {slug} in the request path. tool_version: type: string description: Output-contract version for this tool. credits_used: type: integer description: >- Credits this call consumed, after any settlement refund. 0 when metering is disabled. credits_remaining: type: - integer - 'null' description: >- Credits left in the current monthly allowance, or null when metering is disabled. request_id: type: string description: Correlation id, also sent as x-request-id. '400': $ref: '#/components/responses/ValidationError' '401': $ref: '#/components/responses/Unauthorized' '402': $ref: '#/components/responses/InsufficientCredits' '403': $ref: '#/components/responses/ToolNotAllowed' '404': $ref: '#/components/responses/ToolNotFound' '413': $ref: '#/components/responses/PayloadTooLarge' '429': $ref: '#/components/responses/RateLimited' '500': $ref: '#/components/responses/ToolFailed' '503': $ref: '#/components/responses/ToolDisabled' security: - bearerAuth: [] components: responses: ValidationError: description: Invalid request. content: application/problem+json: schema: type: object description: >- RFC 9457 problem document, served as application/problem+json. Branch on `code`; `title` is human prose and may be reworded without notice. Some failures add extension members — `fields` on validation errors, `retry_after` on 429s, `credits_used`/`credits_remaining` on billing-adjacent failures — documented on the responses that carry them. required: - type - title - status - code properties: type: type: string format: uri description: Stable documentation URI for this failure. examples: - https://iotools.cloud/docs/errors/validation_error title: type: string description: Short human-readable summary of the failure. examples: - Invalid request status: type: integer description: HTTP status code, matching the response's own status. code: type: string description: >- Stable machine-readable error code — branch on this, not `title`. enum: - validation_error detail: type: string description: Human explanation of this occurrence. request_id: type: string description: Correlation id, also sent as x-request-id. fields: type: - object - string additionalProperties: type: string description: >- What failed: a map of field name → message. Absent when the body itself is malformed; a single string when the failure isn't tied to one field. example: type: https://iotools.cloud/docs/errors/validation_error title: Invalid request status: 400 code: validation_error detail: One or more inputs are invalid — see `fields`. request_id: e4042b29-8f1e-4c7a-9b52-6f0d1a3c7e11 fields: inputString: Required Unauthorized: description: Missing or invalid API key. content: application/problem+json: schema: type: object description: >- RFC 9457 problem document, served as application/problem+json. Branch on `code`; `title` is human prose and may be reworded without notice. Some failures add extension members — `fields` on validation errors, `retry_after` on 429s, `credits_used`/`credits_remaining` on billing-adjacent failures — documented on the responses that carry them. required: - type - title - status - code properties: type: type: string format: uri description: Stable documentation URI for this failure. examples: - https://iotools.cloud/docs/errors/invalid_api_key title: type: string description: Short human-readable summary of the failure. examples: - Invalid API key status: type: integer description: HTTP status code, matching the response's own status. code: type: string description: >- Stable machine-readable error code — branch on this, not `title`. enum: - invalid_api_key detail: type: string description: Human explanation of this occurrence. request_id: type: string description: Correlation id, also sent as x-request-id. example: type: https://iotools.cloud/docs/errors/invalid_api_key title: Invalid API key status: 401 code: invalid_api_key detail: 'Provide ''Authorization: Bearer ''.' request_id: e4042b29-8f1e-4c7a-9b52-6f0d1a3c7e11 InsufficientCredits: description: Monthly credit allowance exhausted. content: application/problem+json: schema: type: object description: >- RFC 9457 problem document, served as application/problem+json. Branch on `code`; `title` is human prose and may be reworded without notice. Some failures add extension members — `fields` on validation errors, `retry_after` on 429s, `credits_used`/`credits_remaining` on billing-adjacent failures — documented on the responses that carry them. required: - type - title - status - code properties: type: type: string format: uri description: Stable documentation URI for this failure. examples: - https://iotools.cloud/docs/errors/insufficient_credits title: type: string description: Short human-readable summary of the failure. examples: - Insufficient credits status: type: integer description: HTTP status code, matching the response's own status. code: type: string description: >- Stable machine-readable error code — branch on this, not `title`. enum: - insufficient_credits detail: type: string description: Human explanation of this occurrence. request_id: type: string description: Correlation id, also sent as x-request-id. credits_used: type: integer description: Always 0 — a refused call charges nothing. credits_remaining: type: integer description: Credits left in the allowance — fewer than this call costs. example: type: https://iotools.cloud/docs/errors/insufficient_credits title: Insufficient credits status: 402 code: insufficient_credits detail: This call costs 1 credit and 0 remain in this month's allowance. request_id: e4042b29-8f1e-4c7a-9b52-6f0d1a3c7e11 credits_used: 0 credits_remaining: 0 ToolNotAllowed: description: Tool exists but has no API surface. content: application/problem+json: schema: type: object description: >- RFC 9457 problem document, served as application/problem+json. Branch on `code`; `title` is human prose and may be reworded without notice. Some failures add extension members — `fields` on validation errors, `retry_after` on 429s, `credits_used`/`credits_remaining` on billing-adjacent failures — documented on the responses that carry them. required: - type - title - status - code properties: type: type: string format: uri description: Stable documentation URI for this failure. examples: - https://iotools.cloud/docs/errors/tool_not_allowed title: type: string description: Short human-readable summary of the failure. examples: - Tool not available over the API status: type: integer description: HTTP status code, matching the response's own status. code: type: string description: >- Stable machine-readable error code — branch on this, not `title`. enum: - tool_not_allowed detail: type: string description: Human explanation of this occurrence. request_id: type: string description: Correlation id, also sent as x-request-id. example: type: https://iotools.cloud/docs/errors/tool_not_allowed title: Tool not available over the API status: 403 code: tool_not_allowed detail: >- "Background Remover" is available on iotools.cloud but has no API endpoint. request_id: e4042b29-8f1e-4c7a-9b52-6f0d1a3c7e11 ToolNotFound: description: No such tool. content: application/problem+json: schema: type: object description: >- RFC 9457 problem document, served as application/problem+json. Branch on `code`; `title` is human prose and may be reworded without notice. Some failures add extension members — `fields` on validation errors, `retry_after` on 429s, `credits_used`/`credits_remaining` on billing-adjacent failures — documented on the responses that carry them. required: - type - title - status - code properties: type: type: string format: uri description: Stable documentation URI for this failure. examples: - https://iotools.cloud/docs/errors/tool_not_found title: type: string description: Short human-readable summary of the failure. examples: - Tool not found status: type: integer description: HTTP status code, matching the response's own status. code: type: string description: >- Stable machine-readable error code — branch on this, not `title`. enum: - tool_not_found detail: type: string description: Human explanation of this occurrence. request_id: type: string description: Correlation id, also sent as x-request-id. example: type: https://iotools.cloud/docs/errors/tool_not_found title: Tool not found status: 404 code: tool_not_found detail: No tool with that slug. See GET /v1/tools/list. request_id: e4042b29-8f1e-4c7a-9b52-6f0d1a3c7e11 PayloadTooLarge: description: Body too large. content: application/problem+json: schema: type: object description: >- RFC 9457 problem document, served as application/problem+json. Branch on `code`; `title` is human prose and may be reworded without notice. Some failures add extension members — `fields` on validation errors, `retry_after` on 429s, `credits_used`/`credits_remaining` on billing-adjacent failures — documented on the responses that carry them. required: - type - title - status - code properties: type: type: string format: uri description: Stable documentation URI for this failure. examples: - https://iotools.cloud/docs/errors/payload_too_large title: type: string description: Short human-readable summary of the failure. examples: - Payload too large status: type: integer description: HTTP status code, matching the response's own status. code: type: string description: >- Stable machine-readable error code — branch on this, not `title`. enum: - payload_too_large detail: type: string description: Human explanation of this occurrence. request_id: type: string description: Correlation id, also sent as x-request-id. example: type: https://iotools.cloud/docs/errors/payload_too_large title: Payload too large status: 413 code: payload_too_large detail: Request body exceeds this tool's size limit. request_id: e4042b29-8f1e-4c7a-9b52-6f0d1a3c7e11 RateLimited: description: Per-minute rate limit exceeded. headers: Retry-After: description: Seconds to wait before retrying (RFC 9110 delta-seconds). schema: type: integer content: application/problem+json: schema: type: object description: >- RFC 9457 problem document, served as application/problem+json. Branch on `code`; `title` is human prose and may be reworded without notice. Some failures add extension members — `fields` on validation errors, `retry_after` on 429s, `credits_used`/`credits_remaining` on billing-adjacent failures — documented on the responses that carry them. required: - type - title - status - code properties: type: type: string format: uri description: Stable documentation URI for this failure. examples: - https://iotools.cloud/docs/errors/rate_limited title: type: string description: Short human-readable summary of the failure. examples: - Rate limit exceeded status: type: integer description: HTTP status code, matching the response's own status. code: type: string description: >- Stable machine-readable error code — branch on this, not `title`. enum: - rate_limited detail: type: string description: Human explanation of this occurrence. request_id: type: string description: Correlation id, also sent as x-request-id. retry_after: type: integer description: >- Seconds until the window resets — the same value as the `Retry-After` header. example: type: https://iotools.cloud/docs/errors/rate_limited title: Rate limit exceeded status: 429 code: rate_limited detail: Too many requests. Retry in 30s. request_id: e4042b29-8f1e-4c7a-9b52-6f0d1a3c7e11 retry_after: 30 ToolFailed: description: Tool failed to run. content: application/problem+json: schema: type: object description: >- RFC 9457 problem document, served as application/problem+json. Branch on `code`; `title` is human prose and may be reworded without notice. Some failures add extension members — `fields` on validation errors, `retry_after` on 429s, `credits_used`/`credits_remaining` on billing-adjacent failures — documented on the responses that carry them. required: - type - title - status - code properties: type: type: string format: uri description: Stable documentation URI for this failure. examples: - https://iotools.cloud/docs/errors/processing_error - https://iotools.cloud/docs/errors/internal_error title: type: string description: Short human-readable summary of the failure. examples: - Tool failed to run - Internal error status: type: integer description: HTTP status code, matching the response's own status. code: type: string description: >- Stable machine-readable error code — branch on this, not `title`. enum: - processing_error - internal_error detail: type: string description: Human explanation of this occurrence. request_id: type: string description: Correlation id, also sent as x-request-id. credits_used: type: integer description: >- Always 0 on `processing_error` — a failed run is refunded, floor included. credits_remaining: type: integer description: >- Credits left after the refund. Absent when metering is disabled. example: type: https://iotools.cloud/docs/errors/processing_error title: Tool failed to run status: 500 code: processing_error detail: The tool failed to run. Please try again. request_id: e4042b29-8f1e-4c7a-9b52-6f0d1a3c7e11 credits_used: 0 ToolDisabled: description: Tool temporarily disabled. content: application/problem+json: schema: type: object description: >- RFC 9457 problem document, served as application/problem+json. Branch on `code`; `title` is human prose and may be reworded without notice. Some failures add extension members — `fields` on validation errors, `retry_after` on 429s, `credits_used`/`credits_remaining` on billing-adjacent failures — documented on the responses that carry them. required: - type - title - status - code properties: type: type: string format: uri description: Stable documentation URI for this failure. examples: - https://iotools.cloud/docs/errors/tool_disabled - https://iotools.cloud/docs/errors/api_unconfigured title: type: string description: Short human-readable summary of the failure. examples: - Tool temporarily disabled - API not configured status: type: integer description: HTTP status code, matching the response's own status. code: type: string description: >- Stable machine-readable error code — branch on this, not `title`. enum: - tool_disabled - api_unconfigured detail: type: string description: Human explanation of this occurrence. request_id: type: string description: Correlation id, also sent as x-request-id. example: type: https://iotools.cloud/docs/errors/tool_disabled title: Tool temporarily disabled status: 503 code: tool_disabled detail: This tool is temporarily unavailable. Try again shortly. request_id: e4042b29-8f1e-4c7a-9b52-6f0d1a3c7e11 securitySchemes: bearerAuth: type: http scheme: bearer bearerFormat: iot_live_… ````